Policy Iteration Adaptive Dynamic Programming Research Articles

Dynamic event-triggered control for discrete-time nonlinear Markov jump systems using policy iteration-based adaptive dynamic programming

This paper investigates a dynamic event-triggered optimal control problem of discrete-time (DT) nonlinear Markov jump systems (MJSs) via exploring policy iteration (PI) adaptive dynamic programming (ADP) algorithms. The performance index function (PIF) defined in each subsystem is updated by utilizing an online PI algorithm, and the corresponding control policy is derived via solving the optimal PIF. Then, we adopt neural network (NN) techniques, including an actor network and a critic network, to estimate the iterative PIF and control policy. Moreover, the designed dynamic event-triggered mechanism (DETM) is employed to avoid wasting additional resources when the estimated iterative control policy is updated. Finally, based on the Lyapunov difference method, it is proved that the system stability and the convergence of all signals can be guaranteed under the developed control scheme. A simulation example for DT nonlinear MJSs with two system modes is presented to demonstrate the feasibility of the control design scheme.

Fault-Tolerant Optimal Spacecraft Attitude Maneuver: An Incremental Model Approach

This paper addresses the fault-tolerant optimal attitude control problem for a rigid spacecraft with external disturbance, model uncertainties, and actuator faults. Firstly, the incremental nonlinear control technology is used to simplify the attitude control system into an incremental nominal model with a synthetic uncertainty/fault term that is estimated by a nonsingular terminal sliding mode disturbance observer. Secondly, considering a quadratic performance index, the original fault-tolerant optimal control problem is transformed into a guaranteed performance optimal problem of the nominal model. Benefiting from the simplicity of the incremental model, such a modified optimal control problem is solved online by the modified policy iteration adaptive dynamic programming without any initial stable policy assumption. Finally, the attitude angles of the closed-loop system are proved theoretically to be uniformly ultimately bounded at the desired state by using the Lyapunov methods. Simulation results are given to verify the effectiveness of the proposed fault-tolerant optimal attitude control strategy.

Policy Iteration and Event-Triggered Robust Adaptive Dynamic Programming for Large-Scale Systems

Abstract In this paper, an event-triggered robust optimal control approach is proposed for large-scale systems with both parametric and dynamic uncertainties through robust adaptive dynamic programming, policy iteration, and small-gain techniques. By using the input and output data, the unmeasurable states are reconstructed instead of constructing a Luenberger observer. Starting from an admissible control policy, an event-based feedback control policy is learned to save the communication resources and reduce the number of control updates. The closed-loop stability and the convergence of the proposed algorithm are analyzed by using Lyapunov and small-gain techniques. A practical example of multimachine power systems with governor controllers is given to demonstrate the effectiveness of the proposed method.

A partial policy iteration ADP algorithm for nonlinear neuro-optimal control with discounted total reward

This paper constructs a partial policy iteration adaptive dynamic programming (ADP) algorithm to solve the optimal control problem of nonlinear systems with discounted total reward. Compared with traditional policy iteration ADP algorithm, the approach updates the iterative control law only in a local region of the global system state space. With the benefit of this feature, the overall computational burden at each iteration for processing units can be significantly reduced. Hence, this feature enables our algorithm to be successfully executed on low-performance devices such as smartphones, smartwatches and the Internet of Things (IoT) objects. We provide the convergency analysis to show that the generated sequence of value functions is monotonically nonincreasing and can finally reach a local optimum. In addition, the corresponding local policy space is developed theoretically for the first time. Besides, when the sequence of the local system state spaces is chosen properly, we prove that the developed algorithm is capable of finding the global optimal performance index function for the nonlinear systems. Finally, we present a numerical simulation to demonstrate the effectiveness of the proposed algorithm.

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.

Neuro-Optimal Control for Discrete Stochastic Processes via a Novel Policy Iteration Algorithm

In this paper, a novel policy iteration adaptive dynamic programming (ADP) algorithm is presented which is called “local policy iteration ADP algorithm” to obtain the optimal control for discrete stochastic processes. In the proposed local policy iteration ADP algorithm, the iterative decision rules are updated in a local space of the whole state space. Hence, we can significantly reduce the computational burden for the CPU in comparison with the conventional policy iteration algorithm. By analyzing the convergence properties of the proposed algorithm, it is shown that the iterative value functions are monotonically nonincreasing. Besides, the iterative value functions can converge to the optimum in a local policy space. In addition, this local policy space will be described in detail for the first time. Under a few weak constraints, it is also shown that the iterative value function will converge to the optimal performance index function of the global policy space. Finally, a simulation example is presented to validate the effectiveness of the developed method.

Data-driven optimal tracking control of discrete-time multi-agent systems with two-stage policy iteration algorithm

Herein, a novel adaptive dynamic programming (ADP) algorithm is developed to solve the optimal tracking control problem of discrete-time multi-agent systems. Compared to the classical policy iteration ADP algorithm with two components, policy evaluation, and policy improvement, a two-stage policy iteration algorithm is proposed to obtain the iterative control laws and the iterative performance index functions. The proposed algorithm contains a sub-iteration procedure to calculate the iterative performance index functions at the policy evaluation. The convergence proof for the iterative performance index functions and the iterative control laws are provided. Subsequently, the stability of the closed-loop error system is also provided. Further, an actor-critic neural network (NN) is used to approximate both the iterative control laws and the iterative performance index functions. The actor-critic NN can implement the developed algorithm online without knowledge of the system dynamics. Finally, simulation results are provided to illustrate the performance of our method.

An integrated data-driven Markov parameters sequence identification and adaptive dynamic programming method to design fault-tolerant optimal tracking control for completely unknown model systems

In this paper, an integrated design of data-driven fault-tolerant tracking control is addressed relying on the Markov parameters sequence identification and adaptive dynamic programming techniques. For the unknown model systems, the sequence of Markov parameters together with the covariance of innovation signal is firstly estimated by least square method. After a transformation of value function from stochastic to deterministic, a policy iteration adaptive dynamic programming algorithm is then formulated to find the optimal tracking control law. In order to eliminate the influence of unpredicted faults, an active fault-tolerant supervisory control strategy is further constructed by synthesizing fault detection, isolation, estimation and compensation. All these involved designs are performed in the data-driven manner, and thus avoid the information requirement about system drift dynamics. From the perspective of system operation management, the above integrated control scheme provides a framework to achieve the tracking performance optimization, monitoring and maintaining simultaneously. The effectiveness of these conclusions is finally verified via two case studies.

Discrete-Time Nonzero-Sum Games for Multiplayer Using Policy-Iteration-Based Adaptive Dynamic Programming Algorithms.

In this paper, we investigate the nonzero-sum games for a class of discrete-time (DT) nonlinear systems by using a novel policy iteration (PI) adaptive dynamic programming (ADP) method. The main idea of our proposed PI scheme is to utilize the iterative ADP algorithm to obtain the iterative control policies, which not only ensure the system to achieve stability but also minimize the performance index function for each player. This paper integrates game theory, optimal control theory, and reinforcement learning technique to formulate and handle the DT nonzero-sum games for multiplayer. First, we design three actor-critic algorithms, an offline one and two online ones, for the PI scheme. Subsequently, neural networks are employed to implement these algorithms and the corresponding stability analysis is also provided via the Lyapunov theory. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our proposed approach.

Discrete-Time Optimal Control via Local Policy Iteration Adaptive Dynamic Programming.

In this paper, a discrete-time optimal control scheme is developed via a novel local policy iteration adaptive dynamic programming algorithm. In the discrete-time local policy iteration algorithm, the iterative value function and iterative control law can be updated in a subset of the state space, where the computational burden is relaxed compared with the traditional policy iteration algorithm. Convergence properties of the local policy iteration algorithm are presented to show that the iterative value function is monotonically nonincreasing and converges to the optimum under some mild conditions. The admissibility of the iterative control law is proven, which shows that the control system can be stabilized under any of the iterative control laws, even if the iterative control law is updated in a subset of the state space. Finally, two simulation examples are given to illustrate the performance of the developed method.

A novel optimal tracking control scheme for a class of discrete-time nonlinear systems using generalised policy iteration adaptive dynamic programming algorithm

ABSTRACTIn this paper, a novel iterative adaptive dynamic programming (ADP) algorithm, called generalised policy iteration ADP algorithm, is developed to solve optimal tracking control problems for discrete-time nonlinear systems. The idea is to use two iteration procedures, including an i-iteration and a j-iteration, to obtain the iterative tracking control laws and the iterative value functions. By system transformation, we first convert the optimal tracking control problem into an optimal regulation problem. Then the generalised policy iteration ADP algorithm, which is a general idea of interacting policy and value iteration algorithms, is introduced to deal with the optimal regulation problem. The convergence and optimality properties of the generalised policy iteration algorithm are analysed. Three neural networks are used to implement the developed algorithm. Finally, simulation examples are given to illustrate the performance of the present algorithm.

Generalized Policy Iteration Adaptive Dynamic Programming for Discrete-Time Nonlinear Systems

This paper is concerned with a novel generalized policy iteration algorithm for solving optimal control problems for discrete-time nonlinear systems. The idea is to use an iterative adaptive dynamic programming algorithm to obtain iterative control laws which make the iterative value functions converge to the optimum. Initialized by an admissible control law, it is shown that the iterative value functions are monotonically nonincreasing and converge to the optimal solution of Hamilton-Jacobi-Bellman equation, under the assumption that a perfect function approximation is employed. The admissibility property is analyzed, which shows that any of the iterative control laws can stabilize the nonlinear system. Neural networks are utilized to implement the generalized policy iteration algorithm, by approximating the iterative value function and computing the iterative control law, respectively, to achieve approximate optimal control. Finally, numerical examples are presented to verify the effectiveness of the present generalized policy iteration algorithm.

Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems.

This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.