Optimal strictly positive real controllers using direct optimization

In this paper, we consider the H₂-optimal control problem subject to the constraint that the resulting controller be strictly positive real. A direct numerical optimization approach is adopted in conjunction with a controller parametrization that is linear in the unknown parameters. The SPR constraint is easily expressed at each frequency in the form of a linear inequality. The method is applied to a numerical example from the literature and good results are achieved. In particular, the proposed method is particularly adept at determining low order controllers.     

Design of digital controllers for uncertain chaotic systems using fuzzy logic

A new and systematic method to design digital controllers for uncertain chaotic systems with structured uncertainties is presented in this paper. Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system, while the uncertainties are decomposed such that the uncertain chaotic system can be rewritten as a set of local linear models with an additional disturbed input. Conventional control techniques are utilized to develop the continuous-time controllers first. Then, the digital controllers are obtained as the digital redesign of the continuous-time controllers using the state-matching approach. The performance of the proposed controller design is illustrated through numerical examples.     

On non-fragility of controllers for time delay systems: A numerical approach

In this paper an explicit numerical procedure is proposed to determine the non-fragility of parameters of controllers used to stabilize a class of time delay systems. The proposed procedure finds the largest possible circle inscribed in a stability subregion delimited by a simple closed curve in the plane of the controller parameters. The center of this circle is declared to be the controller’s least fragile parameters. The obtained theoretical results are applied and compared with some of the most relevant examples found in the literature. This illustrates that the proposed procedure improves previous results found in the literature so far.     

Model reduction for control systems with restricted complexity controllers

The problem of reduced-order modelling is considered in connection with the design of restricted complexity controllers. The suggested reduction method develops in two phases: (i) a simple frequency response of the overall feedback control system is determined according to the design specifications; (ii) a reduced-order transference of the controlled plant is obtained by solving a linear set of equations in such a way that its behaviour approximates that of the original plant at frequencies which are meaningful for the overall transfer function derived in the first step (e.g. resonance and cutoff frequencies). An example shows how the procedure yields a reduced-order model suitable for designing robust controllers whereas other standard methods, based on properties of the plant only, fail.     

Adaptive prescribed performance control for nonlinear robotic systems

This paper investigates the problem of asymptotic tracking control of nonlinear robotic systems with prescribed performance. The control strategy is developed based on a modified prescribed performance function (PPF) to guarantee the transient behavior, while the requirements on the accurate initial tracking error in the classical PPF can be remedied. The fuzzy logic system (FLS) is used to approximate the unknown dynamics. In the existing PPF based adaptive control schemes with FLSs, the tracking error does not achieve asymptotic convergence. To address this issue, a robust integral of the sign of the error (RISE) term is incorporated into the control design to reject the FLS approximation errors and external disturbances, such that the asymptotic convergence is achieved. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control scheme.     

Q-learning solution for optimal consensus control of discrete-time multiagent systems using reinforcement learning

This paper investigates a Q-learning scheme for the optimal consensus control of discrete-time multiagent systems. The Q-learning algorithm is conducted by reinforcement learning (RL) using system data instead of system dynamics information. In the multiagent systems, the agents are interacted with each other and at least one agent can communicate with the leader directly, which is described by an algebraic graph structure. The objective is to make all the agents achieve synchronization with leader and make the performance indices reach Nash equilibrium. On one hand, the solutions of the optimal consensus control for multiagent systems are acquired by solving the coupled Hamilton–Jacobi–Bellman (HJB) equation. However, it is difficult to get analytical solutions directly of the discrete-time HJB equation. On the other hand, accurate mathematical models of most systems in real world are hard to be obtained. To overcome these difficulties, Q-learning algorithm is developed using system data rather than the accurate system model. We formulate performance index and corresponding Bellman equation of each agent i. Then, the Q-function Bellman equation is acquired on the basis of Q-function. Policy iteration is adopted to calculate the optimal control iteratively, and least square (LS) method is employed to motivate the implementation process. Stability analysis of proposed Q-learning algorithm for multiagent systems by policy iteration is given. Two simulation examples are experimented to verify the effectiveness of the proposed scheme.     

Sliding mode optimal control for linear systems

This paper addresses the optimal control problem for a linear system with respect to a Bolza–Meyer criterion with a non-quadratic non-integral term. The optimal solution is obtained as a sliding mode control, whereas the conventional linear feedback control fails to provide a causal solution. Performance of the obtained optimal controller is verified in the illustrative example against the conventional LQ regulator that is optimal for the quadratic Bolza–Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode control.     

Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming

In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.     

An optimization approach to static output-feedback control of LTI positive systems with delayed measurements

In this paper, we investigate the static output-feedback stabilization problem for LTI positive systems with a time-varying delay in the state and output vectors. By exploiting the induced monotonicity, necessary and sufficient conditions ensuring exponential stability of the closed-loop system are first quoted. Based on the derived stability conditions, necessary and sufficient stabilization conditions are formulated in terms of matrix inequalities. This general setting is then transformed into suitable vertex optimization problems by which necessary and sufficient conditions for the existence of a desired static output-feedback controller are obtained. The proposed synthesis conditions are presented in the form of linear programming conditions, which can be effectively solved by various convex algorithms.     

Some numerical tests for an alternative approach to optimal feedback control

We test a recently proposed approach to optimal feedback control of nonlinear systems leading to an iterative descending strategy [24]. We start by discussing the numerical implementation of this strategy, and propose a number of improvements that can speed up the computation process by up to two orders of magnitude. The resulting algorithm is then applied to a series of test problems of increasing complexity. Results seem to show that this can be a promising strategy to bear in mind for more realistic situations.     

Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach

This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.     

Non-fragile control of positive Markovian jump systems

This paper investigates the non-fragile control for positive Markovian jump systems both in continuous-time and discrete-time cases with actuator uncertainty. It is assumed that the coefficient matrices of the non-fragile controller is unknown and bounded. The state-feedback controller gain consists of nominal controller gain and gain perturbation. First, a set of state-feedback controllers for the considered system are designed by using a stochastic co-positive Lyapunov function integrated with linear programming approach. Under the designed controllers, the resulting closed-loop systems are positive and stochastically stable. Then, the proposed controller design approach is extended to discrete-time systems. Through comparisons, it is shown that existing results are special cases of the presented ones in the paper. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

A survey Of learning-Based control of robotic visual servoing systems

Major difficulties and challenges of modern robotics systems focus on how to give robots self-learning and self-decision-making ability. Visual servoing control strategy is an important strategy of robotic systems to perceive the environment via the vision. The vision can guide new robotic systems to complete more complicated tasks in complex working environments. This survey aims at describing the state-of-the-art learning-based algorithms, especially those algorithms that combine with model predictive control (MPC) used in visual servoing systems, and providing some pioneering and advanced references with several numerical simulations. The general modeling methods of visual servo and the influence of traditional control strategies on robotic visual servoing systems are introduced. The advantages of introducing neural-network-based algorithms and reinforcement-learning-based algorithms into the systems are discussed. Finally, according to the existing research progress and references, the future directions of robotic visual servoing systems are summarized and prospected.     

A comparative study of optimal linear controllers for vibration suppression

The performance enhancement of dynamic systems is accomplished by the application of active control components. Control strategies are derived to accomplish the task. Among the various control strategies, those that are designed to minimize a specified cost function while satisfying the necessary system constraints are referred to as optimal controllers. An important constraint is the amount of power and energy consumed by the control device. In this paper, the effect of optimal control strategies on the power and energy requirement of control devices is investigated.     

Dynamic event-triggered optimal tracking control for constrained nonlinear stochastic systems

This paper investigates the optimal tracking control problem (OTCP) for nonlinear stochastic systems with input constraints under the dynamic event-triggered mechanism (DETM). Firstly, the OTCP is converted into the stabilizing optimization control problem by constructing a novel stochastic augmented system. The discounted performance index with nonquadratic utility function is formulated such that the input constraint can be encoded into the optimization problem. Then the adaptive dynamic programming (ADP) method of the critic-only architecture is employed to approximate the solutions of the OTCP. Unlike the conventional ADP methods based on time-driven mechanism or static event-triggered mechanism (SETM), the proposed adaptive control scheme integrates the DETM to further lighten the computing and communication loads. Furthermore, the uniform ultimately boundedness (UUB) of the critic weights and the tracking error are analysed with the Lyapunov theory. Finally, the simulation results are provided to validate the effectiveness of the proposed approach.     

Adaptive neural network control for flexible telerobotic systems with communication constraints

This paper investigates the synchronous control problem for a class of flexible telerobotic systems subject to system uncertainties and communication constraints. In view of the asymmetric time-varying communication delays, an adaptive time-delay estimator is designed to reduce the impacts of delays on the system. Moreover, by combining the neural networks and parameter adaptive method, the uncertainties of system dynamics are estimated and compensated. Based on these efforts, a new adaptive compensation control protocol is proposed. Additionally, input quantization in network control induced chattering phenomenon and unknown parameters is also dealt with by the adaptive compensation method. A useful characteristic of this paper is that the “complexity explosion” problem caused by the backstepping technique is circumvented effectively. Finally, sufficient conditions are derived for the synchronous control of the master-slave flexible telerobotic system under Lyapunov stability theory. A numerical example of flexible-joint robotic system is provided to illustrate the effectiveness of the proposed control schemes.     

Synchronization control for multiple heterogeneous robotic systems with parameter uncertainties and communication delays

This paper investigates synchronization of multiple heterogeneous robotic systems (MHRSs) in the presence of kinematic uncertainties, dynamic uncertainties and communication delays. We develop two classes of adaptive sliding-mode controllers to deal with the aforementioned problem based on directed graphs containing a directed spanning tree, which relaxes the constraints on the interaction topologies. Furthermore, by invoking techniques of Lyapunov and input-output stability theories, we obtain the sufficient conditions on asymptotic stability of MHRSs. Thus, the position and velocity synchronization errors can asymptotically converge to the origin. Finally, numerous simulations are carried out to demonstrate the validity and advantages of the theoretical results.     

Fault tolerant cooperative control for affine multi-agent systems: An optimal control approach

The goal of this paper is to propose an optimal fault tolerant control (FTC) approach for multi-agent systems (MASs). It is assumed that the agents have identical affine dynamics. The underlying communication topology is assumed to be a directed graph. The concepts of both inverse optimality and partial stability are further employed for designing the control law fully developed in the paper. Firstly, the optimal FTC problem for linear MASs is formulated and then it is extended to MASs with affine nonlinear dynamics. To solve the Hamilton-Jacobi-Bellman (HJB) equation, an Off-policy Reinforcement Learning is used to learn the optimal control law for each agent. Finally, a couple of numerical examples are provided to demonstrate the effectiveness of the proposed scheme.     

Robust adaptive visual tracking control for uncertain robotic systems with unknown dead-zone inputs

This paper is concerned with the image-based visual servoing (IBVS) control for uncalibrated camera-robot system with unknown dead-zone constraint, where the uncertain kinematics and dynamics are also considered. The control implementation is achieved by constructing a smooth inverse model for dead-zone-input to eliminate the nonlinear effect resulting from the actuator constraint. A novel adaptive algorithm, which does not require a priori knowledge of the parameter intervals of dead-zone model, is proposed to update the parameter values online, and the dead-zone slopes are not required the same. Furthermore, to accommodate the uncertainties of uncalibrated camera-robot system, adaptation laws are developed to estimate the uncertain parameters, simultaneously avoiding singularity of the image Jacobian matrix. With the full consideration of unknown dead-zone constraint and system uncertainties, an adaptive robust visual tracking control scheme together with dead-zone compensation is subsequently established such that the image tracking error converges to the origin. Based on a 3-DOF manipulator, simulations are conducted to verify the tracking performance of the proposed controller.