arXiv subjects

Hongdan Li

Publications and source records attributed to Hongdan Li.

17 recordsLinked to original sources

arXiv2025

Finite-Horizon Discrete-Time Optimal Control for Nonlinear Systems under State and Control Constraints

This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior computational efficiency, with the novelty lying in establishing a unified framework that integrates all aspects of algorithm design through the solution of forward and backward difference equations (FBDEs). Firstly, the state and control constraints are transformed using an augmented Lagrangian method (ALM), thereby decomposing the original optimal control problem into several optimization subproblems. These subproblems are then reformulated as new optimal control problem, which are solved through the corresponding FBDEs, resulting in an algorithm with superlinear convergence rate. Furthermore, the gradient and Hessian matrix are computed by iteratively solving FBDEs, thereby accelerating the optimization process. The gradient is obtained through the standard Hamiltonian, while the Hessian matrix is derived by constructing a novel Hamiltonian specifically designed for second-order optimization, transforming each row into an iterative solution of a new set of FBDEs. Finally, the effectiveness of the algorithm is validated through simulation results in automatic guided vehicles (AGV) trajectory tracking control.

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arXiv2024

Optimal Control of Discrete-Time Nonlinear Systems

This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time constraints. While linearization methods are computationally efficient, their inherent low accuracy can compromise control precision and overall performance. To address this challenge, this study proposes a novel approach based on the optimal control method. Firstly, the original optimal control problem is transformed into an equivalent optimization problem, which is resolved using the Pontryagin's maximum principle, and a superlinear convergence algorithm is presented. Furthermore, to improve computation efficiency, explicit formulas for computing both the gradient and hessian matrix of the cost function are proposed. Finally, the effectiveness of the proposed algorithm is validated through simulations and experiments on a linear quadratic regulator problem and an automatic guided vehicle trajectory tracking problem, demonstrating its ability for real-time online precise control.

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arXiv2024

A General Method for Optimal Decentralized Control with Current State/Output Feedback Strategy

This paper explores the decentralized control of linear deterministic systems in which different controllers operate based on distinct state information, and extends the findings to the output feedback scenario. Assuming the controllers have a linear state feedback structure, we derive the expression for the controller gain matrices using the matrix maximum principle. This results in an implicit expression that couples the gain matrices with the state. By reformulating the backward Riccati equation as a forward equation, we overcome the coupling between the backward Riccati equation and the forward state equation. Additionally, we employ a gradient descent algorithm to find the solution to the implicit equation. This approach is validated through simulation examples.

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arXiv2023

Reinforcement Learning for Stochastic LQ Control of Discrete-Time Systems with Multiplicative Noises

This paper considers a stochastic linear quadratic problem for discrete-time systems with multiplicative noises over an infinite horizon. To obtain the optimal solution, we propose an online iterative algorithm of reinforcement learning based on Bellman dynamic programming principle. The algorithm avoids the direct calculation of algebra Riccati equations. It merely takes advantage of state trajectories over a short interval instead of all iterations, significantly simplifying the calculation process. Under the stabilizable initial values, numerical examples shed light on our theoretical results.

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arXiv2023

Private Inputs for Leader-Follower Game with Feedback Stackelberg Strategy

In this paper, the two-player leader-follower game with private inputs for feedback Stackelberg strategy is considered. In particular, the follower shares its measurement information with the leader except its historical control inputs while the leader shares none of the historical control inputs and the measurement information with the follower. The private inputs of the leader and the follower lead to the main obstacle, which causes the fact that the estimation gain and the control gain are related with each other, resulting that the forward and backward Riccati equations are coupled and making the calculation complicated. By introducing a kind of novel observers through the information structure for the follower and the leader, respectively, a kind of new observer-feedback Stacklberg strategy is designed. Accordingly, the above-mentioned obstacle is also avoided. Moreover, it is found that the cost functions under the presented observer-feedback Stackelberg strategy are asymptotically optimal to the cost functions under the optimal feedback Stackelberg strategy with the feedback form of the state. Finally, a numerical example is given to show the efficiency of this paper.

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arXiv2023

An Approach to Mismatched Disturbance Rejection Control for Continuous-Time Uncontrollable Systems

This paper focuses on optimal mismatched disturbance rejection control for linear continuoustime uncontrollable systems. Different from previous studies, by introducing a new quadratic performance index to transform the mismatched disturbance rejection control into a linear quadratic tracking problem, the regulated state can track a reference trajectory and minimize the influence of disturbance. The necessary and sufficient conditions for the solvability and the disturbance rejection controller are obtained by solving a forward-backward differential equation over a finite horizon. A sufficient condition for system stability is obtained over an infinite horizon under detectable condition. This paper details our novel approach for transforming disturbance rejection into a linear quadratic tracking problem. The effectiveness of the proposed method is provided with two examples to demonstrate.

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arXiv2022

Closed-Loop Stackelberg Strategy for Linear-Quadratic Leader-Follower Game

This paper is concerned with the closed-loop Stackelberg strategy for linear-quadratic leader-follower game. Completely different from the open-loop and feedback Stackelberg strategy, the solvability of the closed-loop solution even the linear case remains challenging. The main contribution of the paper is to derive the explicitly linear closed-loop Stackelberg strategy with one-step memory in terms of Riccati equations. The key technique is to apply the constrained maximum principle to the leader-follower game and explicitly solve the corresponding forward and backward difference equations. Numerical examples verify the effectiveness of the results, which achieves better performance than feedback strategy.

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arXiv2022

An Approach to Mismatched Disturbance Rejection Control for Uncontrollable Systems

This study focuses on the problem of optimal mismatched disturbance rejection control for uncontrollable linear discrete-time systems. In contrast to previous studies, by introducing a quadratic performance index such that the regulated state can track a reference trajectory and minimize the effects of disturbances, mismatched disturbance rejection control is transformed into a linear quadratic tracking problem. The necessary and sufficient conditions for the solvability of this problem over a finite horizon and a disturbance rejection controller are derived by solving a forward-backward difference equation. In the case of an infinite horizon, a sufficient condition for the stabilization of the system is obtained under the detectable condition. This paper details our novel approach to disturbance rejection. Four examples are provided to demonstrate the effectiveness of the proposed method.

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arXiv2020

Optimal Control for Discrete-time NCSs with Input Delay and Markovian Packet Losses: Hold-Input Case

This paper is concerned with the linear quadratic optimal control problem for networked system simultaneously with input delay and Markovian dropout. Different from the results in the literature, we consider the hold-input strategy, which is much more computationally complicated than zero-input strategy, but much better in most cases especially in the transition phase. Necessary and sufficient conditions for the solvability of optimal control problem over a finite horizon are given by the coupled difference Riccati-type equations. Moreover, the networked control system is mean-square stability if and only if the coupled algebraic Riccati-type equations have a particular solution. The key technique in this paper is to tackle the forward and backward difference equations, which are more difficult to be dealt with, due to the adaptability of controller and the temporal correlation caused by simultaneous input delay and Markovian jump.

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arXiv2019

Stabilization Control for ItO Stochastic System with Indefinite State and Control Weight Costs

In standard linear quadratic (LQ) control, the first step in investigating infinite-horizon optimal control is to derive the stabilization condition with the optimal LQ controller. This paper focuses on the stabilization of an Ito stochastic system with indefinite control and state weighting matrices in the cost functional. A generalized algebraic Riccati equation (GARE) is obtained via the convergence of the generalized differential Riccati equation (GDRE) in the finite-horizon case. More importantly, the necessary and sufficient stabilization conditions for indefinite stochastic control are obtained. One of the key techniques is that the solution of the GARE is decomposed into a positive semi-definite matrix that satisfies the singular algebraic Riccati equation (SARE) and a constant matrix that is an element of the set satisfying certain linear matrix inequality conditions. Using the equivalence between the GARE and SARE, we reduce the stabilization of the general indefinite case to that of the definite case, in which the stabilization is studied using a Lyapunov functional defined by the optimal cost functional subject to the SARE.

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arXiv2019

Optimal Control Problem for Discrete-Time Systems with Colored Multiplicative Noise

The optimal control problem for discrete-time systems with colored multiplicative noise is discussed in this paper. The problem will be more difficult to deal with than the case of white noise due to the correlation of the adjoining state. By solving the forward and backward stochastic difference equations (FBSDEs), the necessary and sufficient conditions for the solvability of the optimal control problems in both delay-free and one-step input delay case are given.

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arXiv2019

Deterministic Optimal Control of Ito Stochastic Systems with Random Coefficients

This paper is concerned with the deterministic optimal control of Ito stochastic systems with random coefficients. The necessary and sufficient conditions for the unique solvability of the optimal control problem with random coefficients are derived via the solution to the coupled stochastic Riccati-type equations. An explicit expression of the deterministic optimal controller for this problem is given. The presented results include the case of deterministic coefficient [14] as special case.

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arXiv2019

Optimal Stabilization Control for Discrete-time Markov Jump Linear System with Control Input Delay

This paper will investigate the infinite horizon optimal control and stabilization problems for the Markov jump linear system (MJLS) subject to control input delay. Different from previous works, for the first time, the necessary and sufficient stabilization conditions are explored under explicit expressions, and the optimal controller for infinite horizon is designed with a coupled algebraic Riccati equation. By introducing a new type of Lyapunov equation, we show that under the exact observability assumption, the MJLS with control input delay is stabilizable in the mean square sense with the optimal controller if and only if a coupled algebraic Riccati equation has a unique positive definite solution. The presented results are parallel to the optimal control and stabilization for standard system with input delay.

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arXiv2018

Stabilization for Networked Control Systems with Simultaneous Input Delay and Markovian Packet Losses

The mean square stabilization problem for discrete-time networked control systems (NCSs) is investigated in this article. What the difference from most previous works is that input delay and packet losses occur simultaneously in the communication channel, moreover, the data packet dropout is modeled as a time-homogeneous Markov process which will bring some difficulties in solving the problem due to the temporal correlation. The contributions in this paper can be summarized as two points. Firstly, the equivalence condition for the solvability of linear quadratic optimal problem in finite horizon subject to the discrete-time NCSs is expressed by solving the forward and backward stochastic difference equations (FBSDEs-M) which is derived from the maximum principle involving Markov jump and delay. Secondly, under basic assumption, the necessary and sufficient condition of mean square stabilization is given by the solutions to the coupled algebraic Riccati equations with Markov jump (CAREs-M). To our best knowledge, the problems studied in this paper are new because most previous works mainly discussed the case of only delay or packet dropout in NCSs.

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arXiv2018

Optimal Control for Discrete-time Markov Jump Linear System with Control Input Delay

This paper deals with the finite horizon optimal control problem for discrete-time Markov jump linear system with input delay. The correlation among the jumping parameters and the input delay are considered simultaneously, which forms the basic difficulty of the design. one of the key techniques is to solve a delayed forward and backward jumping parameter difference equation which is obtained by an improved maximum principle, and the other is the introduction of a "d-step backward formula". Based on the proposed techniques, a necessary and sufficient condition for the existence of the optimal controller is given in an explicit form and an analytical solution to the optimal controller is supplied. The optimal controller is a linear function of the current time state and the historical time control input, where the feedback gains are a set of jumping parameter matrices derived by solving a new type of coupled difference Riccati equation. The key step in the derivation is to establish the relationship between the costate and the real state of the system. The result obtained in this paper can be viewed as a generalization of the standard case, in which there is only one mode of operation.

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arXiv2018

Optimal Control and Stabilization Problem for Discrete-time Markov Jump Systems with Indefinite Weight Costs

It is well known that stability is the most fundamental nature with regard to a control system, in view of this, the stabilization becomes an inevitable control problem. This article mainly discusses the optimal control and stabilization problem for discrete-time systems involving Markov jump and multiplicative noise. The state and control weighting matrices in the cost function are allowed to be indefinite. By solving the forward-backward stochastic difference equations with Markov jump (FBSDEs-MJ) derived from the maximum principle, we conclude that the necessary and sufficient conditions of the solvability of indefinite optimal control problem in finite-horizon, whose method is different from most previous works [13], etc. Furthermore, necessary and sufficient conditions that stabilize the Markov jump discrete- time systems in the mean square sense with indefinite weighting matrices in the cost are first developed under the basic assumption of exactly observable, which is different from the previous works [12], [14] where an additional assumption of stabilization of systems is made. The key points of this article can be summed up as that an analytic solution to FBSDEs- MJ which makes the optimal controller to be explicitly expressed and the method of trans- formation, i.e., the stabilization problem of indefinite case is boiled down to a definite one whose stabilization is expressed by defining Lyapunov function via the optimal cost subject to a new algebraic Riccati equation involving Markov jump (NGARE-MJ).

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arXiv2018

Linear Quadratic Optimal Control and Stabilization for Discrete-time Markov Jump Linear Systems

This paper mainly investigates the optimal control and stabilization problems for linear discrete-time Markov jump systems. The general case for the finite-horizon optimal controller is considered, where the input weighting matrix in the performance index is just required to be positive semi-definite. The necessary and sufficient condition for the existence of the optimal controller in finite-horizon is given explicitly from a set of coupled difference Riccati equations (CDRE). One of the key techniques is to solve the forward and backward stochastic difference equation (FDSDE) which is obtained by the maximum principle. As to the infinite-horizon case, we establish the necessary and sufficient condition to stabilize the Markov jump linear system in the mean square sense. It is shown that the Markov jump linear system is stabilizable under the optimal controller if and only if the associated couple algebraic Riccati equation (CARE) has a unique positive solution. Meanwhile, the optimal controller and optimal cost function in infinite-horizon case are expressed explicitly.

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