Disturbance observer-based robust missile autopilot design with full-state constraints via adaptive dynamic programming

This paper aims to develop a robust optimal control method for longitudinal dynamics of missile systems with full-state constraints suffering from mismatched disturbances by using adaptive dynamic programming (ADP) technique. First, the constrained states are mapped by smooth functions, thus, the considered systems become nonlinear systems without state constraints subject to unknown approximation error. In order to estimate the unknown disturbances, a nonlinear disturbance observer (NDO) is designed. Based on the output of disturbance observer, an integral sliding mode controller (ISMC) is derived to counteract the effects of disturbances and unknown approximation error, thus ensuring the stability of nonlinear systems. Subsequently, the ADP technique is utilized to learn an adaptive optimal controller for the nominal systems, in which a critic network is constructed with a novel weight update law. By utilizing the Lyapunov's method, the stability of the closed-loop system and the convergence of the estimation weight for critic network are guaranteed. Finally, the feasibility and effectiveness of the proposed controller are demonstrated by using longitudinal dynamics of a missile.     

Task-space control for industrial robot manipulators with unknown inner loop control architecture

The operational space control of a robot manipulator using external sensors requires stabilizing the compound system {external sensors - outer controller - inner controller - robot manipulator}. The user must access the inner controller to reshape it to achieve this stabilization. Due to intellectual property protection purposes, most industrial robots have an unknown or inaccessible inner controller. Therefore, it is tricky to design a stable control scheme. To solve this problem, an adaptive radial basis function neural network (RBF NN) outer controller is proposed, which approximates the inner controller’s dynamics to eliminate its effect in the closed-loop. An inherent property for RBF NN is used to reduce the number of adaptive parameters. Since this technique introduces approximation errors, it is included in the control scheme, a term that constrains the system to converge rapidly to the performances prescribed by the user. It is proved that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB) through Lyapunov theory. The effectiveness of the proposed approach is verified through simulation comparisons and experimental studies.     

Distributed cooperative controller design considering guidance loop and impact angle

This paper presents an integrated distributed cooperative guidance and control scheme for multiple missiles to attack a single target simultaneously at desired impact angles. The scheme is divided into two parts: individual part and cooperative part. For the individual part, partial integrated guidance and control method is adopted to generate the elevator deflection (which is a realistic control input) to ensure that the missiles fly along their respective desired line of sight and hit the target; this is in contrast to previous works which analyze only the engagement dynamics and use missile accelerations as the control input, however, the proposed controller also considers the missile dynamics, thus enabling the implementation of an autopilot. For the cooperative part, using only information from adjacent missiles, the proposed distributed cooperative controller can make all missiles hit the target simultaneously. Hence in this scheme, each missile can hit the target at desired angles and at the same time, thus achieving salvo attack. Simulations are performed to verify the effectiveness of the scheme.     

Neural networks-based adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances

This paper focuses on the problem of adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances. Radial basis function neural networks (NNs) are employed to approximate the unknown functions and an NN observer is constructed to estimate the unmeasurable system states. Moreover, an auxiliary system is introduced to compensate for the effect of input delay. With the aid of the backstepping technique and Lyapunov stability theorem, an adaptive NN output feedback controller is designed which can guarantee the boundedness of all the signals in the closed-loop systems. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Neural-network-based fault-tolerant control for nonlinear systems subjected to faults and saturations

This paper investigates a novel strategy which can address the fault-tolerant control (FTC) problem for nonlinear strict-feedback systems containing actuator saturation, unknown external disturbances, and faults related to actuators and components. In such method, the unknown dynamics including faults and disturbances are approximated by resorting to Neural-Networks (NNs) technique. Meanwhile, a back-stepping technique is employed to build a fault-tolerant controller. It should be stressed that the main advantage of this strategy is that the NN weights are updated online based on gradient descent (GD) algorithm by minimizing the cost function with respect to NNs approximation error rather than regarding weights as adaptive parameters, which are designed according to Lyapunov theory. In addition, the convergence proof of NN weights and the stability proof of the proposed FTC method are given. Finally, simulation is performed to demonstrate the effectiveness of the proposed strategy in dealing with unknown external disturbances, actuator saturation and the faults related to the components and actuators, simultaneously.     

Pattern-based NN control for uncertain pure-feedback nonlinear systems

Implementing human-like learning and control for nonlinear dynamical systems operating in different control situations is an important and challenging issue. This paper presents a pattern-based neural network (NN) control strategy for nonlinear pure-feedback systems via deterministic learning (DL). Firstly, an appropriately designed adaptive neural dynamic surface controller is proposed to achieve the finite time tracking control. By analyzing the recurrent property of NN input signals, a partial persistent excitation (PE) condition for radial basis function (RBF) network is established, the implicit desired control dynamics under different control situations are accurately identified via DL in the case that the dimension of NN input is reduced. And a set of pattern-based experienced actual and virtual controllers is constructed using the learned knowledge. Secondly, to classify different control situations, when the system is operating in different control situations but controlled by current normal experienced controller, the dynamics of each subsystem are accurately identified via DL, n sets of dynamical estimators are constructed using the learned knowledge. Thirdly, in the recognition phase, n sets of residuals are achieved by comparing each set of estimators with the monitored system, sudden change in the control situation is rapidly recognized based on the principle of the earliest occurrence of the minimum residual. Finally, in the control phase, according to the recognition result, the correct experienced actual and virtual controllers will be selected to control the plant, guaranteed stability and superior control performance are achieved without any further re-adaptation online. Simulation studies are given to verify the proposed scheme can not only acquire and memorize knowledge like humans, but also reuse the learned knowledge to achieve rapid recognition and control of current control situation.     

Adaptive fuzzy sliding mode command-filtered backstepping control for islanded PV microgrid with energy storage system

This study focuses on the control of islanded photovoltaic (PV) microgrid and design of a controller for PV system. Because the system operates in islanded mode, the reference voltage and frequency of AC bus are provided by the energy storage system. We mainly designed the controller for PV system in this study, and the control objective is to control the DC bus voltage and output current of PV system. First, a mathematical model of the PV system was set up. In the design of PV system controller, command-filtered backstepping control method was used to construct the virtual controller, and the final controller was designed by using sliding mode control. Considering the uncertainty of circuit parameters in the mathematical model and the unmodeled part of PV system, we have integrated adaptive control in the controller to achieve the on-line identification of component parameters of PV system. Moreover, fuzzy control was used to approximate the unmodeled part of the system. In addition, the projection operator guarantees the boundedness of adaptive estimation. Finally, the control effect of designed controller was verified by MATLAB/Simulink software. By comparing with the control results of proportion-integral (PI) and other controllers, the advanced design of controller was verified.     

Predictor-based optimal robust guaranteed cost control for uncertain nonlinear systems with completely tracking errors constraint

In this paper, a novel composite controller is proposed to achieve the prescribed performance of completely tracking errors for a class of uncertain nonlinear systems. The proposed controller contains a feedforward controller and a feedback controller. The feedforward controller is constructed by incorporating the prescribed performance function (PPF) and a state predictor into the neural dynamic surface approach to guarantee the transient and steady-state responses of completely tracking errors within prescribed boundaries. Different from the traditional adaptive laws which are commonly updated by the system tracking error, the state predictor uses the prediction error to update the neural network (NN) weights such that a smooth and fast approximation for the unknown nonlinearity can be obtained without incurring high-frequency oscillations. Since the uncertainties existing in the system may influence the prescribed performance of tracking error and the estimation accuracy of NN, an optimal robust guaranteed cost control (ORGCC) is designed as the feedback controller to make the closed-loop system robustly stable and further guarantee that the system cost function is not more than a specified upper bound. The stabilities of the whole closed-loop control system is certified by the Lyapunov theory. Simulation and experimental results based on a servomechanism are conducted to demonstrate the effectiveness of the proposed method.     

Online adaptive policy iteration based fault-tolerant control algorithm for continuous-time nonlinear tracking systems with actuator failures

In this paper, a novel tracking control scheme for continuous-time nonlinear affine systems with actuator faults is proposed by using a policy iteration (PI) based adaptive control algorithm. According to the controlled system and desired reference trajectory, a novel augmented tracking system is constructed and the tracking control problem is converted to the stabilizing issue of the corresponding error dynamic system. PI algorithm, generally used in optimal control and intelligence technique fields, is an important reinforcement learning method to solve the performance function by critic neural network (NN) approximation, which satisfies the Lyapunov equation. For the augmented tracking error system with actuator faults, an online PI based fault-tolerant control law is proposed, where a new tuning law of the adaptive parameter is designed to tolerate four common kinds of actuator faults. The stability of the tracking error dynamic with actuator faults is guaranteed by using Lyapunov theory, and the tracking errors satisfy uniformly bounded as the adaptive parameters get converged. Finally, the designed fault-tolerant feedback control algorithm for nonlinear tracking system with actuator faults is applied in two cases to track the desired reference trajectory, and the simulation results demonstrate the effectiveness and applicability of the proposed method.     

Actuator failure compensation and attitude control for rigid satellite by adaptive control using quaternion feedback

The attitude control problem of a rigid satellite with actuator failure uncertainties and external disturbance is addressed using adaptive control method. A discontinuous adaptive failure compensation controller, using unit quaternion and angular velocities feedback, is designed to accommodate the external disturbance and actuator failures which are uncertain in time instants, values and patterns. A common approximate function is used to avoid system chattering caused by such discontinuous control laws. The parameters of external disturbance and failure uncertainties are estimated directly by adaptive laws, and the desired stability and output tracking properties of the adaptive control system are analyzed. Finally, simulation results of a rigid satellite with six reaction wheels are presented to illustrate the performance of the proposed adaptive actuator failure compensation scheme.     

Decentralized adaptive neural control for interconnected stochastic nonlinear delay-time systems with asymmetric saturation actuators and output constraints

This paper investigates the problem of decentralized adaptive backstepping control for a class of large-scale stochastic nonlinear time-delay systems with asymmetric saturation actuators and output constraints. Firstly, the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are designed to ensure that the output parameters are restricted. Secondly, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities. At last, based on Lyapunov stability theory, a decentralized adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters. It is shown that the designed controller can ensure that all the closed-loop signals are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two examples are provided to show the effectiveness of the proposed method.     

Optimal adaptive reset control with guaranteed transient and steady state tracking error bounds

In this paper, a solution for improvement of transient performance in adaptive control of nonlinear systems is proposed. An optimal adaptive controller based on a reset mechanism and a prescribed performance bound is devised. The suggested controller has the structure of adaptive backstepping controller in which the estimated parameters are reset to an optimal value. The designed controller ensures both the transient bound and the asymptotical convergence of the states. It is shown that the tracking error satisfies the prescribed performance bound all the time, besides the speed of the convergence rate is increased by resetting the estimated parameters. The results have been proved through both the analytical and simulation studies. The proposed method is applied to an Augmented Quarter Car Model as a case study. Simulation results verify the established theoretical consequences that the prescribed performance bound based optimal adaptive reset controller can enhance the transient performance of the adaptive controller.     

An update algorithm design using moving Region of Attraction for SDRE based control law

State Dependent Riccati Equation (SDRE) methods have the considerable advantages over other nonlinear control methods. However, stability issues can be arisen in SDRE based control system due to the lack of the global asymptotic stability property. Therefore, the previous studies have usually shown that local asymptotic stability can be ensured by estimating a Region of Attraction (ROA) around the equilibrium point. These estimated regions for stability may become narrow or the condition to keep the states in this region may be very conservative. To resolve these issues, this paper proposes a novel SDRE method employing an update algorithm to re-estimate the ROA when the states tend to move out of the stable region. The tendency is checked using a condition which is developed based on a new theorem. The theorem proves that it is possible to redesign the previous ROA with respect to the current states lying close to its boundary for ensuring the “non-local” stability along the trajectory without the need of solving SDRE at each time instant, unlike the standard SDRE approach. Therefore, the new theorem is now able to enhance the stability of the SDRE based closed-loop control system. The feasibility of the proposed SDRE control method is tested in both simulations and experiments. A validated 3-DOF laboratory helicopter is used for experiments and the control objective for the helicopter is to realise a preplanned movement in both elevation and travel axes. The results reveal that the proposed SDRE approach enables the controlled plant to track the desired trajectory as satisfactorily as the standard SDRE approach, while only solving SDRE when needed. The proposed SDRE method reduces the computational load for practical implementation of the control algorithm whilst ensuring the stability over the operational region.     

Design and analysis of a novel cascade control algorithm for braking-by-wire system based on electromagnetic direct-drive valves

In order to improve the response speed and control precision of the braking system with parameters uncertainty and nonlinear friction, a braking-by-wire system based on the electromagnetic direct-drive valve and a novel cascade control algorithm was proposed in this paper. An electromagnetic linear actuator directly drives the valve spool and rapidly adjusts the pressure of braking wheel cylinders. A dynamic model of electromagnetic direct-drive valve considering improved LuGre dynamic friction is established. A novel cascade control algorithm with an outside loop pressure fuzzy controller and an inside loop electromagnetic direct-drive valve position controller was proposed. An adaptive integral robust inside loop controller is designed by combining friction compensation adaptive control law, linear feedback, and integral robust control. The uncertainty parameters and the friction state are estimated online. The stability of the cascade controller is proved by the Lyapunov method. Then a multi-objective opitimizemization design method of control parameters is proposed, which combines a multi-objective game theory and a technique for order preference by similarity to ideal solution (TOPSIS) based on entropy weight. The results show that the pressurization time of cascade control is less than 0.09 s under the 15 MPa step target signal. The control precision is improved effectively by the cascade controller under the ARTEMIS condition.     

Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation

This paper develops a robust adaptive neural network (NN) tracking control scheme for a class of strict-feedback nonlinear systems with unknown nonlinearities and unknown external disturbances under input saturation. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the uncertain system dynamics. The adaptive laws are designed to online update the upper bound of the norm of ideal NN weight vectors, and the sum of the bounds of NN approximation errors and external disturbances, respectively. An auxiliary dynamic system is constructed to generate the augmented error signals which are used to modify the adaptive laws for preventing the destructive action due to the input saturation. Moreover, the command filtering backstepping control method is utilized to overcome the shortcoming of dynamic surface control method, the tracking-differentiator-based control method, etc. Our proposed scheme is qualified for simultaneously dealing with the input saturation effect, the heavy computational burden and the “explosion of complexity” problems. Theoretical analysis illuminates that our scheme ensures the boundedness of all signals in the closed-loop systems. Simulation results on two examples verify the effectiveness of our developed control scheme.     

A novel controller for nonlinear uncertain systems using a combination of SDRE and function approximation technique: Regulation and tracking of flexible-joint manipulators

This paper presents a novel combined State Dependent Riccati Equation (SDRE) / Function Approximation Technique (FAT)-based control design for nonlinear uncertain systems. The SDRE is employed to construct an optimal controller and the function approximation technique is utilized to estimate time-varying disturbances and uncertainties. Moreover, a robust term in the proposed control law compensates for the truncation error. The closed-loop stability and boundedness of the tracking error and FAT weights approximation error are proved in the sense of Lyapunov, with consideration of truncation error. Due to the great importance of the adequate performance of transient response from practical point of view, performance evaluation has been accomplished. The proposed scheme is computationally simple due to utilizing the FAT to represent uncertainties and disturbances as a function of time. Compared with the SDRE based SMC, the proposed controller is superior in terms of capability to track a fast and highly complicated trajectory and no need to determine time-varying disturbances and uncertainties bounds. The case study is a Selective Compliant Articulated Robot for Assembly (SCARA) flexible joint manipulator as a representative of highly nonlinear, coupled, large robotic systems. Simulation results easily verify the effectiveness and superiority of the proposed controller.     

Semi-globally/globally stable adaptive NN backstepping control for uncertain MIMO systems with tracking accuracy known a priori

This paper focuses on the problem of direct adaptive neural network (NN) tracking control for a class of uncertain nonlinear multi-input/multi-output (MIMO) systems by employing backstepping technique. Compared with the existing results, the outstanding features of the two proposed control schemes are presented as follows. Firstly, a semi-globally stable adaptive neural control scheme is developed to guarantee that the ultimate tracking errors satisfy the accuracy given a priori, which cannot be carried out by using all existing adaptive NN control schemes. Secondly, we propose a novel adaptive neural control approach such that the closed-loop system is globally stable, and in the meantime the ultimate tracking errors also achieve the tracking accuracy known a priori, which is different from all existing adaptive NN backstepping control methods where the closed-loop systems can just be ensured to be semi-globally stable and the ultimate tracking accuracy cannot be determined a priori by the designers before the controllers are implemented. Thirdly, the main technical novelty is to construct three new nth-order continuously differentiable switching functions such that multiswitching-based adaptive neural backstepping controllers are designed successfully. Fourthly, in contrast to the classic adaptive NN control schemes, this paper adopts Barbalat׳s lemma to analyze the convergence of tracking errors rather than Lyapunov stability theory. Consequently, the accuracy of ultimate tracking errors can be determined and adjusted accurately a priori according to the real-world requirements, and all signals in the closed-loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the two proposed adaptive NN control schemes.     

Cooperative control problem of Takagi-Sugeno fuzzy multiagent systems via observer based distributed adaptive sliding mode control

In this paper, the consensus control problem of Takagi-Sugeno (T-S) fuzzy multiagent systems (MASs) is investigated by using an observer based distributed adaptive sliding mode control. A distributed nonfragile observer is put forward to estimate the unmeasured state of agents. Based on such an observer, a novel distributed integral sliding surface is designed to suppress the disturbance and uncertainty of T-S fuzzy MASs. In order to achieve the consensus objective, a nominal distributed protocol and an adaptive sliding mode controller are separately designed. Futhermore, the nominal distributed protocol solves the consensus control problem of T-S fuzzy MASs in the absence of disturbance and uncertainty by using the information of adjacent agents obtained by the observer, while the adaptive sliding mode controller suppresses the disturbance and uncertainty. Finally, the proposed method is applied to two examples. Example 1 verifies the superiority of the method by comparing with the fuzzy-based dynamic sliding mode controller. Example 2 is used to illustrate that our control scheme can effectively solve the consensus control problem of T-S fuzzy MASs.     

Optimized sliding mode current controller for power converters with non-minimum phase nature

This paper proposes a unified method to design an optimized type of the hysteresis modulation-based sliding mode current controller for non-minimum phase power converters in continuous conduction mode. The traditional sliding mode controlled converters have a slow transient voltage response at heavy loads, a large overshoot at light loads and during abrupt output resistance variations. To solve these problems, an optimized feedback control scheme is used according to the output resistance to adjust the coefficients of the controller. The basic idea of this controller is to suggest a new way for reduction of the sensitivity function amplitude of the closed loop system. The presented approach is developed for three basic DC/DC converters; i.e. boost, buck-boost and quadratic boost converters. Generally, the certain advantages of the suggested control approach are: (i) a fast transient response can be achieved in heavy load conditions, (ii) the voltage overshoot can be effectively reduced during load variations; (iii) the transient voltage overshoot can be eliminated in light load conditions; (iv) the closed loop control sensitivity can be reduced and therefore, the performance specification of a control system can be improved compared with the conventional sliding mode current control. To show the reliability of the suggested control scheme, simulations and experimental results for the derived systems are developed. Several conditions are performed to confirm the effectiveness of the proposed controller.     

Event-triggered-based adaptive dynamic programming for distributed formation control of multi-UAV

This paper is concerned with the distributed formation control problem of multi-quadrotor unmanned aerial vehicle (UAV) in the framework of event triggering. First, for the position loop, an adaptive dynamic programming based on event triggering is developed to design the formation controller. The critic-only network structure is adopted to approximate the optimal cost function. The merit of the proposed algorithm lies in that the event triggering mechanism is incorporated the neural network (NN) to reduce calculations and actions of the multi-UAV system, which is significant for the practical application. What’s more, a new weight update law based on the gradient descent technology is proposed for the critic NN, which can ensure that the solution converges to the optimal value online. Then, a finite-time attitude tracking controller is adopted for the attitude loop to achieve rapid attitude tracking. Finally, the efficiency of the proposed method is illustrated by numerical simulations and experimental verification.