scholarly journals Backward Stochastic Riccati Equation with Jumps Associated with Stochastic Linear Quadratic Optimal Control with Jumps and Random Coefficients

2020 ◽  
Vol 58 (1) ◽  
pp. 393-424 ◽  
Author(s):  
Fu Zhang ◽  
Yuchao Dong ◽  
Qingxin Meng
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
Random Coefficients ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Backward Stochastic Riccati Equation ◽  
Quadratic Optimal Control ◽  
Stochastic Riccati Equation

scholarly journals Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Avinash Kumar ◽  
Tushar Jain
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Riccati Equation ◽  
Nonconvex Optimization ◽  
Optimization Problem ◽  
A Priori ◽  
Control Law ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control

This paper revisits the problem of synthesizing the optimal control law for linear systems with a quadratic cost. For this problem, traditionally, the state feedback gain matrix of the optimal controller is computed by solving the Riccati equation, which is primarily obtained using calculus of variations- (CoV-) based and Hamilton–Jacobi–Bellman (HJB) equation-based approaches. To obtain the Riccati equation, these approaches require some assumptions in the solution procedure; that is, the former approach requires the notion of costates and then their relationship with states is exploited to obtain the closed-form expression of the optimal control law, while the latter requires a priori knowledge regarding the optimal cost function. In this paper, we propose a novel method for computing linear quadratic optimal control laws by using the global optimal control framework introduced by V. F. Krotov. As shall be illustrated in this article, this framework does not require the notion of costates and any a priori information regarding the optimal cost function. Nevertheless, using this framework, the optimal control problem gets translated to a nonconvex optimization problem. The novelty of the proposed method lies in transforming this nonconvex optimization problem into a convex problem. The convexity imposition results in a linear matrix inequality (LMI), whose analysis is reported in this work. Furthermore, this LMI reduces to the Riccati equation upon imposing optimality requirements. The insights along with the future directions of the work are presented and gathered at appropriate locations in this article. Finally, numerical results are provided to demonstrate the proposed methodology.

scholarly journals Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Xikui Liu ◽  
Guiling Li ◽  
Yan Li
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
Discrete Time ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Discrete Time Systems ◽  
Quadratic Optimal Control ◽  
The Cost ◽  
Time Systems ◽  
Difference Riccati Equation

The Karush-Kuhn-Tucker (KKT) theorem is used to study stochastic linear quadratic optimal control with terminal constraint for discrete-time systems, allowing the control weighting matrices in the cost to be indefinite. A generalized difference Riccati equation is derived, which is different from those without constraint case. It is proved that the well-posedness and the attainability of stochastic linear quadratic optimal control problem are equivalent. Moreover, an optimal control can be denoted by the solution of the generalized difference Riccati equation.

scholarly journals The Delayed Doubly Stochastic Linear Quadratic Optimal Control Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yan Chen ◽  
Jie Xu
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Riccati Equation ◽  
Control Variable ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Doubly Stochastic ◽  
Quadratic Optimal Control

In this paper, the delayed doubly stochastic linear quadratic optimal control problem is discussed. It deduces the expression of the optimal control for the general delayed doubly stochastic control system which contained time delay both in the state variable and in the control variable at the same time and proves its uniqueness by using the classical parallelogram rule. The paper is concerned with the generalized matrix value Riccati equation for a special delayed doubly stochastic linear quadratic control system and aims to give the expression of optimal control and value function by the solution of the Riccati equation.

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