Distributed MPC-based adaptive control for linear systems with unknown parameters

This paper is concerned with the adaptive control problem for a class of linear discrete-time systems with unknown parameters based on the distributed model predictive control (MPC) method. Instead of using the system state, the state estimate is employed to model the distributed state estimation system. In this way, the system state does not have to be measurable. Furthermore, in order to improve the system performance, both the output error and its estimation are considered. Moreover, a novel Lyapunov functional, comprised of a series of distributed traces of estimation errors and their transposes, has been presented. Then, sufficient conditions are obtained to guarantee the exponential ultimate boundedness of the system as well as the asymptotic stability of the error system by solving a nonlinear programming (NP) problem subject to input constraints. Finally, the simulation examples is given to illustrate the effectiveness and the validity of the proposed technique.     

Model reference adaptive control for switched linear systems using switched multiple models control strategy

In this paper, the multiple model strategy is applied to the adaptive control of switched linear systems to improve the transient performance. The solvability of the adaptive stabilization problem of each subsystem is not required. Firstly, the two-layer switching mechanism is designed. The state-dependent switching law with dwell time constraint is designed in the outer-layer switching to guarantee the stability of the switched systems. During the interval of dwell time constraint, the parameter resetting adaptive laws are designed in the inner-layer switching to improve the transient performance. Secondly, the minimum dwell time constraint providing enough time for multiple model adaptive control strategy to work fully and maintaining the stability of the switched systems is found. Finally, the proposed switched multiple model adaptive control strategy guarantees that all the closed-loop system signals remain bounded and the state tracking error converges to zero.     

Decentralized adaptive tracking quantized control for interconnected pure feedback time delay nonlinear systems

This paper focuses on the problem of adaptive tracking quantized control for a class of interconnected pure feedback time delay nonlinear systems. To satisfy the requirement of prescribed performance on the output tracking error, a novel asymmetric tangent barrier Lyapunov function is developed. The decentralized adaptive controller is designed via backstepping method. To deal with the uncertain interconnected nonlinear functions, we design a new virtual control input in the first step. Instead of estimating the bound of each unknown function, we use the adaptive method to estimate the bound of the composite function which is composed of the unknown functions. Thus the over parameterization problem is avoided. It is proved that the output of each subsystem satisfies the prescribed performance requirement and other state variables are bounded. Finally, the simulations are performed and the results verify the effectiveness of the proposed method.     

Data-driven adaptive optimal control of linear uncertain systems with unknown jumping dynamics

This paper focuses on the optimal control of a DC torque motor servo system which represents a class of continuous-time linear uncertain systems with unknown jumping internal dynamics. A data-driven adaptive optimal control strategy based on the integration of adaptive dynamic programming (ADP) and switching control is presented to minimize a predefined cost function. This takes the first step to develop switching ADP methods and extend the application of ADP to time-varying systems. Moreover, an analytical method to give the initial stabilizing controller for policy iteration ADP is proposed. It is shown that under the proposed adaptive optimal control law, the closed-loop switched system is asymptotically stable at the origin. The effectiveness of the strategy is validated via simulations on the DC motor system model.     

A novel adaptive robust control approach for underactuated mobile robot

Underactuated mobile robot (UMR) is a typical nonlinear underactuated system with nonholonomic and holonomic constraints. Based on the model of UMR, we propose a novel adaptive robust control to control the UMR and compensate the uncertainties from the view of constraint-following. The uncertainties, which are (possibly fast) time-varying and bounded, include modeling error, initial condition deviation, friction force and other external disturbances. However, the bounds are unknown. To estimate the bounds of the uncertainties, we design an adaptive law which is of leakage type. The uniform boundedness and the uniform ultimate boundedness of the proposed control are verified by Lyapunov method. Furthermore, the effectiveness of the control is shown via numerical simulation of a case.     

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.     

Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems

In this paper, the issues of finite-time extended dissipative analysis and non-fragile control are investigated for a class of uncertain discrete time switched linear systems. Based on average dwell-time approach, sufficient conditions for the finite-time boundedness and finite-time extended dissipative performance of the considered systems are proposed by solving some linear matrix inequalities, where using the concept of extended dissipative, we can solve the H_∞, $L_2?L_{\infty },$ Passivity and (Q, S, R)-dissipativity performance in a unified framework. Furthermore, two form of non-fragile state feedback controllers are designed to guarantee that the closed-loop systems satisfy the finite-time extended dissipative performance. Finally, simulation example is given to show the efficiency of the proposed methods.     

Learning control for linear systems under general data dropouts at both measurement and actuator sides: A Markov chain approach

This paper contributes to the convergence analysis of iterative learning control for linear systems under general data dropouts at both measurement and actuator sides. By using a simple compensation mechanism for the dropped data, the sample path behavior along the iteration axis is analyzed and formulated as a Markov chain first. Based on the Markov chain, the recursion of the input error is reformulated as a switching system, and then a novel convergence proof is established in the almost sure sense under mild design conditions. Illustrative examples are provided to verify the theoretical results.     

Distributed adaptive event-triggered protocol for tracking control of leader-following multi-agent systems

A novel adaptive event-triggered control protocol is developed to investigate the tracking control problem of multi-agent systems with general linear dynamics. By introducing the event-triggered control strategy, each agent can decide when to transfer its state to its neighbors at its own triggering instants, which can greatly reduce communication burden of agents. It is shown that the “Zeno phenomenon” does not occur by verifying that there exists a positive lower bound on the inter-event time intervals of agents under the proposed adaptive event-triggered control algorithm. Finally, an example is provided to testify the effectiveness of the obtained theoretical results.     

TS fuzzy robust L1 control for nonlinear systems with persistent bounded disturbances

In this paper, a novel technique for Takagi–Sugeno (TS) model-based robust L₁ controller design of nonlinear systems is proposed. Two synthesis methods based on quadratic and non-quadratic Lyapunov functions are considered. To design the robust stabilizing controller, a new approach for deriving sufficient conditions associated with the L₁ performance criterion in terms of strict linear matrix inequality is proposed. This novel technique results in less pre-chosen scalar design variables and calculation burden. Furthermore, deriving the controller synthesis conditions via a non-quadratic Lyapunov function (NQLF) relaxes the obtained conditions. Therefore, the proposed approaches not only efficiently minimize the effect of persistent bounded disturbance, but also are applicable for wider classes of TS systems. Furthermore, some new lemmas are proposed to facilitate strict LMI formulation and to provide more degrees of freedom. Finally, several numerical and practical examples are presented to show the merits of this paper.     

Observer-based event-triggered tracking consensus of non-ideal general linear multi-agent systems

In this paper, the leader-following consensus problem of general linear multi-agent systems without direct access to real-time state is investigated. A novel observer-based event-triggered tracking consensus control scheme is proposed. In the control scheme, a distributed observer is designed to estimate the relative full states, which are used in tracking consensus protocol to achieve overall consensus. And an event-triggered mechanism with estimated state-dependent event condition is adopted to update the control signals so as to reduce unnecessary data communication. Based on the Lyapunov theorem and graph theory, the proposed event-triggered control scheme is proved to implement the tracking consensus when real-time state cannot direct obtain. Moreover, such scheme can exclude Zeno-behavior. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

Online partitioning method for decentralized control of linear switching large-scale systems

A novel partitioning approach for linear switching large-scale systems is presented. We assume that the modes of the switching system are unknown a priori but can be detected. We propose an online partitioning scheme that can partition the system when the mode switches, thus adapting the partition to the mode. Moreover, after the system has been partitioned, we apply a decentralized state-feedback control scheme to stabilize the system. We also apply a dwell time stability scheme to prove that the closed-loop system remains stable even after both the mode and partition changes. The proposed approach is illustrated by means of an automatic generation control problem related to frequency deviation regulation in a large-scale power network.     

Synchronization for chaotic systems via mixed-objective dynamic output feedback robust model predictive control

This paper focuses on mixed-objective dynamic output feedback robust model predictive control (OFRMPC) for the synchronization of two identical discrete-time chaotic systems with polytopic uncertainties, energy bounded disturbances, and input constraint. Using active control strategy, the chaos synchronization is transformed into standard dynamic OFRMPC scenarios tractable through receding horizon min–max optimization. Utilizing the notion of quadratic boundedness, the augmented closed-loop stability is further characterized. Then, the concepts of mixed performance criteria are firstly incorporated into the dynamic OFRMPC scheme to guarantee both the robust stability and the disturbance attenuation ability while preserving better dynamical behaviors. Necessary and/or sufficient conditions for desired mixed-objective dynamic OFRMPC are formulated involving linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the theoretical results.     

Command filter-based finite-time adaptive fuzzy control for nonlinear systems with uncertain disturbance

In this paper, a command filter-based adaptive fuzzy controller is constructed for a class of nonlinear systems with uncertain disturbance. By using the error compensation signals and fuzzy logic system, a command filter-based control strategy is presented to make that the tracking error converge to an any small neighborhood of zero and all closed-loop signals are bounded. In the design procedure, fuzzy logic system is employed to estimate unknown package nonlinear functions, which avoids excessive and burdensome computations. The control scheme not only resolves the explosion of complexity problem but also eliminates the filtering error in finite-time. An example has evaluated the validity of the control method.     

Event-triggered adaptive fault-tolerant control for nonlinear systems fusing static and dynamic information

In this paper, a novel event-triggered adaptive fault-tolerant control scheme is proposed for a class of nonlinear systems with unknown actuator faults. Multiplicative faults and additive faults are taken into account simultaneously, both of which may vary with time. Different from existing results, our controller fuses static reliability information and dynamic online information, which is helpful to enhance the fault-tolerant capability. With the aid of an event-triggering mechanism, an actuator switching strategy and a bound estimation approach, the communication burden is significantly reduced and the impacts of the actuator faults as well as the network-induced error are effectively compensated for. Moreover, by employing the prescribed performance control technique, the system tracking error can converge to a predefined arbitrarily small residual set with prescribed convergence rate and maximum overshoot, which implies that the proposed scheme is able to ensure rapid and accurate tracking. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Finite-time adaptive control for a class of switched stochastic uncertain nonlinear systems

This paper addresses the problem of global finite-time adaptive control for a class of switched stochastic uncertain nonlinear systems under arbitrary switchings. By applying the delicate introduction of coordinate transformations and adding a power integrator technique, an adaptive controller is constructed to guarantee that the system state is regulated to the origin almost surely in a finite time while maintaining the boundedness of the resulting closed-loop systems in probability. Two examples are given to illustrate the effectiveness of the proposed control scheme.     

Improved approaches on adaptive event-triggered output feedback control of networked control systems

This paper studies the static output-feedback control in a class of networked control systems. Different from the existing results, the transmission of control signals is based on a novel adaptive event-triggered scheme, where the adaptive thresholds depend on the dynamic error of the system rather than predetermined constants as the traditional ones. The amount of the releasing data is regulated by the adaptive thresholds that play an essential role in decision of whether releasing the sampled data or not. Through fully using the information on network-induced delay and introducing two adjusting parameters, an augmented Lyapunov–Krasovskii (L–K) functional is constructed. Especially, some novel Wirtinger-based integral inequalities are utilized to reconsider those previously ignored information, which can help reduce the conservatism. Furthermore, a novel constructive method is developed to obtain the controller gain by solving the achieved linear matrix inequalities (LMIs). Finally, three numerical examples are given to illustrate the efficiency of the presented results.     

Output feedback adaptive robust control of hydraulic actuator with friction and model uncertainty compensation

This paper studies output feedback control of hydraulic actuators with modified continuous LuGre model based friction compensation and model uncertainty compensation. An output feedback adaptive robust controller is constructed which combines the adaptive control part and the robust control part seamlessly. The adaptive part is constructed to handle the parametric uncertainties existed in the model. The residuals coming from parameter adaption and the unmodeled dynamics are taken into consideration by the robust part. Since only the position signal is available, the velocity, pressure, and internal friction states are obtained by observation or estimation. The errors coming from observation and estimation are also dealt with the robust part. Furthermore, the convergence of the closed-loop controller–observer scheme is achieved by the Lyapunov method in the presence of parametric uncertainties only. Extensive comparative experiments performed on a hydraulic actuator demonstrate the effectiveness of the proposed controller–observer scheme.     

Iterative learning control for linear delay systems with deterministic and random impulses

This paper investigates convergence of iterative learning control for linear delay systems with deterministic and random impulses by virtute of the representation of solutions involving a concept of delayed exponential matrix. We address linear delay systems with deterministic impulses by designing a standard P-type learning law via rigorous mathematical analysis. Next, we extend to consider the tracking problem for delay systems with random impulses under randomly varying length circumstances by designing two modified learning laws. We present sufficient conditions for both deterministic and random impulse cases to guarantee the zero-error convergence of tracking error in the sense of Lebesgue-p norm and the expectation of Lebesgue-p norm of stochastic variable, respectively. Finally, numerical examples are given to verify the theoretical results.