Distributed Optimal Output Feedback Control of Heterogeneous Multi-agent Systems under a Directed Graph

This paper investigates the optimal couple-group consensus control (OCGCC) for heterogeneous multi-agent systems (HeMASs) with completely unknown dynamics. The agents in HeMASs are divided into two groups according to order differences. Meanwhile, heterogeneous systems are transformed into homogeneous ones by adding virtual velocities. Then, a novel data-driven distributed control protocol for HeMASs is proposed based on policy gradient reinforcement learning (RL). The proposed algorithm is implemented asynchronously, and is specifically designed to address the issue of computational imbalance caused by individual differences among participants. It achieves this by constructing an actor-critic (AC) framework. The system’s learning efficacy is optimized using offline data sets. The convergence and stability are ensured by applying functional analysis and the Lyapunov stability theory. Finally, the effectiveness of the proposed algorithm is confirmed by various simulation examples.

Finite-time partial stability and stabilization, and optimal feedback control

The optimal control with an ergodic cost function is investigated for a class of stochastic discrete‐time linear systems with unknown system coefficient matrices. We present an online value iteration‐based stochastic adaptive dynamic programming algorithm to obtain the approximation sequence of the optimal state feedback control gain and rigorously prove that the approximation sequence converges to the optimal state feedback control gain under some reasonable conditions. In the framework of direct adaptive control, the diminishing excitation technique is introduced for an unknown stochastic discrete‐time state space model, and we prove that the adaptive controller, which is given by real‐time computation, is optimal. In contrast to existing related results, our method does not need to collect enough data to solve the Bellman equation in each iteration and avoids the requirement to estimate means and variances of controllers or states. A numerical simulation is provided to evaluate the efficacy of the presented approach.

Drug Administration in Cancer Treatment via Optimal Nonlinear State Feedback Gain Matrix Design

A stochastic minimax optimal time-delay state feedback control strategy for uncertain quasi-integrable Hamiltonian systems is proposed. First, a stochastic optimal state feedback control problem of uncertain quasi-integrable Hamiltonian system with time delay in feedback control subjected to Gaussian white noise is formulated. Then, the time-delayed state feedback control forces are approximated by the control forces without time delay and the original problem is converted into a stochastic optimal state feedback control problem of an uncertain system without time delay. After that, by following a procedure based on the stochastic averaging method and stochastic differential game, the worst-case disturbances and the optimal controls are obtained from solving a Hamiltonian–Jacobi–Isaacs (HJI) equation. As an example, the stochastic minimax optimal state feedback control of a Duffing oscillator with parametric disturbances and time-delayed feedback control is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy.

In this paper, we study the optimal control problem for Takagi–Sugeno (T-S) fuzzy systems with disturbances. Due to the presence of disturbances in the T-S fuzzy systems, a fuzzy optimal state feedback control approach is presented by employing a two-player zero-sum game. Since the analytical optimal control solutions and the worst-case disturbance policies of T-S fuzzy systems can be boiled down to solving the algebraic Riccati equations (AREs), which are difficult to be obtained directly, a model-free policy iteration (PI) learning algorithm is proposed to obtain their approximation solutions. It is proved that the developed fuzzy optimal state feedback controller can ensure the fuzzy systems to be asymptotically stable and satisfy the disturbance attenuation condition simultaneously. Also, the designed PI learning algorithm can converge to their optimal solutions. Finally, we apply the developed fuzzy optimal state feedback control method to the truck-trailer system and the simulation results demonstrated the effectiveness of the developed scheme.

This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems. Unlike existing optimal state feedback control, the control input of the optimal parallel control is introduced into the feedback system. However, due to the introduction of control input into the feedback system, the optimal state feedback control methods can not be applied directly. To address this problem, an augmented system and an augmented performance index function are proposed firstly. Thus, the general nonlinear system is transformed into an affine nonlinear system. The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically. It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function. Moreover, an adaptive dynamic programming ( ADP ) technique is utilized to implement the optimal parallel tracking control using a critic neural network ( NN ) to approximate the value function online. The stability analysis of the closed-loop system is performed using the Lyapunov theory, and the tracking error and NN weights errors are uniformly ultimately bounded ( UUB ) . Also, the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals. Finally, the effectiveness of the developed optimal parallel control method is verified in two cases.

This paper addresses active vibration control of adaptive structures using piezoelectric active structural elements with built-in sensing and actuation function. Optimal placement and feedback gain of these active members are important issues, which are discussed in this study. An efficient optimal placement strategy has been developed using minimum control energy dissipating over infinite time interval. Optimal location of active members has been found through minimization of total control energy dissipating over infinite time interval using Simulated Annealing (SA) algorithm. Moreover, the effect of structural randomness and random load in optimal feedback gain has been investigated. To accomplish this, a mathematical model with reliability constraints on the stress and displacement is developed and the optimal velocity feedback gain of active members, using probabilistic optimization technique, is obtained. Illustrative examples are presented to demonstrate the effectiveness of this methodology. It is shown that deterministic approach can not provide reliable optimum design values.

Data-based adaptive neural network optimal output feedback control for nonlinear systems with actuator saturation

This paper presents a now method of optimal digital PID feedback control for a linear multivariate system by using a, parameter optimization technique. The most difficult points for the design of optimal digital PID feedback control system by the modern control theory are : (1) the control structure of it is specified in advance, (2) unless all the state variables are fed back, the optimal control cannot be obtained by dynamic programming or the maximum principle. However, the optimal digital PID feedback gains are determined by using the parameter optimization technique in this paper. When there are some states which are not fed back in the control system, the optimal feedback gains depend on the initial states. First, the optimal solution is presented in the case where all the initial Btates are known. Next, it is extended to the case where the initial states are random variables and their statistical properties are known,

This paper presents as its main result a new and efficient method for the design of optimal dynamic compensators for linear multivariable control systems. The discussion starts with a fresh look into the design of optimal constant gain output feedback. In this context, three new ideas are introduced that prove their usefulness particularly in the dynamic compensator case: (1) deterministic measurement disturbances are included in the formulation of the underlying optimization problem, (2) the relationship between a deterministic and a stochastic optimal control problem is shown, (3) by proper modifications of the quadratic cost function, the effort involved in the numerical solution of the optimal output feedback problem is considerably reduced. Furthermore, a canonical form is introduced for the dynamic compensator and an algorithm is developed for the numerical computation of its free parameters. It is based on quasi-newtonian gradient methods and an efficient line search procedure. Some features of the new design method are demonstrated by means of a non-trivial benchmark taken from the literature.

Perhaps the most widely used results in optimal control theory are those related to the control of linear systems. In this chapter we concentrate on finding steady-state optimal feedback controller gains for linear time-invariant systems. Here, the cost functional minimized is quadratic in the state and control variables. Section 8.2 considers the optimal state feedback controller gain problem, section 8.3 addresses the optimal output feedback problem, and section 8.4 treats the more general optimal dynamic compensator problem.

The problem of resilient optimal bipartite tracking control for heterogeneous multi-agent systems with multiple targets under denial-of-service (DoS) attacks is investigated in this paper. A bipartite tracking mechanism is devised in which the agents track the targets under bipartite consensus control, which becomes non-autonomous. This is owing to DoS attacks, as the agents cannot obtain real-time information on the tracked targets and neighboring agents. Consequently, A target observer with a storage module has been developed for the efficient estimation of agent states and the storage of observed information as historical data. By recalling the historical data of the observed state, a new type of distributed resilient optimal controller is formulated, which can achieve the control objective in the case of communication blockage, while minimizing the performance index function of the system. Numerical simulations are performed to verify the proposed secure control design.

Learning-based optimal cooperative control using edge-based triggering strategy

This article deals with the problem of optimal static output feedback control of linear periodic systems in continuous time, for which a continuous-time approach, which allows to deal with both stable and unstable open loop systems, is presented. The proposed approach is tested on the problem of designing attitude control laws for a Low-Earth Orbit (LEO) satellite on the basis of feedback from a triaxial magnetometer and a set of high-precision gyros. Simulation results are used to demonstrate the feasibility of the proposed strategy and to evaluate its performance.