Stable iterative optimal control for discrete-time nonlinear systems using numerical controller

In this paper, a novel iterative adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. When the iterative control law and iterative performance index function in each iteration cannot be accurately obtained, it is shown that the iterative controls can make the performance index function converge to within a finite error bound of the optimal performance index function. Stability properties are presented to show that the system can be stabilized under the iterative control law which makes the present iterative ADP algorithm feasible for implementation both on-line and off-line. Neural networks are used to approximate the iterative performance index function and compute the iterative control policy, respectively, to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

In this paper, a novel value iteration adaptive dynamic programming (ADP) algorithm, called "generalized value iteration ADP" algorithm, is developed to solve infinite horizon optimal tracking control problems for a class of discrete-time nonlinear systems. The developed generalized value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. Convergence property is developed to guarantee that the iterative performance index function will converge to the optimum. Neural networks are used to approximate the iterative performance index function and compute the iterative control policy, respectively, to implement the iterative ADP algorithm. Finally, a simulation example is given to illustrate the performance of the developed algorithm.

In this paper, an iterative adaptive dynamic programming (ADP) algorithm is developed to solve the optimal cooperative control problems for residential multi-battery systems. To avoid solving high-dimensional optimal control problems, we first constrain all the batteries at their worst performance, which transforms the multi-input optimal control problem into a single-input one. Based on the worst-performance optimal control law, the optimal cooperative control law for the residential multi-battery systems is obtained, where in each iteration, only a single-input optimization problem is implemented. Finally, numerical results are given to illustrate the performance of the developed algorithm.

This paper deals with optimal tracking control problems for a class of discrete-time nonlinear systems using a generalized policy iteration adaptive dynamic programming (ADP) algorithm. First, by system transformation, the optimal tracking control problem is transformed into an optimal regulation problem. Then the generalized policy iteration ADP algorithm is employed to obtain the optimal tracking controller with convergence and optimality analysis. The developed algorithm uses the idea of two iteration procedures to obtain the iterative tracking control laws and the iterative value functions. Three neural networks, including model network, critic network and action network, are used to implement the developed algorithm. At last, an simulation example is given to demonstrate the effectiveness of the developed method.

Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach

Neural-network-based output-feedback control with stochastic communication protocols

In this paper, an on-line adaptive dynamic programming (ADP) algorithm is presented to solve the optimal control problem for continuous-time nonlinear systems with control constraints. First, a suitable non-quadratic performance function is introduced to confront control constraints, and then we present an on-line ADP algorithm in which dynamic programming techniques and neural networks are used to solve the optimal control problem for nonlinear systems with control constraints, which is completely different with the traditional ADP algorithm using off-line training, and the corresponding convergence proof is given. Finally, a simulation examples is given to demonstrate the convergence and feasibility of the proposed algorithm.

In this paper, a new iterative optimal learning control scheme for discrete-time nonlinear systems using iterative adaptive dynamic programming (ADP) approach is developed to obtain the optimal control law for coal gasification control systems. For the unknown coal gasification process, neural networks (NNs) are introduced to reconstruct the dynamics of the gasification process, where the approximation errors of the reconstruction dynamics are considered. Via system transformation, the optimal tracking control problem with approximation errors is transformed into a two-person zero-sum optimal control problem. A new iterative ADP algorithm is then developed to obtain the optimal control law for the transformed system with convergence analysis. Finally, numerical results are given to illustrate the performance of the present method.

Adaptive dynamic programming for security of networked control systems with actuator saturation

An iterative adaptive dynamic programming algorithm for optimal control of unknown discrete-time nonlinear systems with constrained inputs

In this paper, an optimal tracking control approach based on adaptive dynamic programming (ADP) algorithm is proposed to solve the linear quadratic regulation (LQR) problems for unknown discrete-time systems in an online fashion. First, we convert the optimal tracking problem into designing infinite-horizon optimal regulator for the tracking error dynamics based on the system transformation. Then we expand the error state equation by the history data of control and state. The iterative ADP algorithm of policy iteration (PI) and value iteration (VI) are introduced to solve the value function of the controlled system. It is shown that the proposed ADP algorithm solves the LQR without requiring any knowledge of the system dynamics. The simulation results show the convergence and effectiveness of the proposed control scheme.

In this paper, a new generalized policy iteration (GPI) based adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems. The GPI algorithm is a general idea of interacting policy and value iteration algorithms of ADP. There are two iteration indices, which iterate for policy improvement and policy evaluation, respectively, in the GPI algorithm. The convergence properties of the GPI algorithm are developed. Finally, simulation results are presented to illustrate the performance of the developed algorithm.

In this paper, a finite-horizon ε-optimal control for a class of nonlinear systems with state delay is proposed by Adaptive Dynamic Programming (ADP) algorithm. First of all, the performance index function is defined and the Hamilton-Jacobi-Bellman (HJB) equation is obtained for the problem, the convergence of the iterative algorithm is also presented. Then, ADP algorithm for finite-horizon optimal control is introduced with an ε-error bound so as to get the ε-optimal control, and BP neural network is used to implement ADP algorithm. At last, an example is given to demonstrate the effectiveness of the proposed algorithm.

This paper studies an online adaptive dynamic programming (ADP) algorithm for linear fixed-time impulse systems. The ADP algorithm follows the value iteration method, updating the value approximation and the control law iteratively. In the algorithm, a single network structure is adopted. The single critic network approximates the objective value function. Online training of the value function and the control laws are implemented at each iteration. The network approximated value function converges to the optimal one of the impulse system. Simulations are also presented for the validity of the presented algorithm.

Robust oxygen excess ratio control of PEMFC systems using adaptive dynamic programming