2 Stochastic optimal control (discrete time) 2 2.1 The Linear-quadratic-Gaussian (LQG) case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Message passing in LQG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Special case: kinematic control . . . . . . . . . . . . . . . . . . . . . . . . . ...

A new algorithmic setting is proposed for the discrete-time finite-horizon linear quadratic (LQ) optimal control problem with constrained or unconstrained final state, no matter whether the problem is cheap, singular, or regular. The proposed solution, based on matrix pseudoinversion, is completed and made practically implementable by a nesting procedure for welding optimal subarcs that enables...

The paper considers a discrete-time linear quadratic Gaussian model with constrained control. It is formulated with Markov systems. With the derivative equation, a performance gradient with respect to control parameters is estimated from a sample path. Then a learning algorithm is proposed to obtain a suboptimal feedback policy in affine linear form. The learning algorithm can be implemented on...

In this paper we study the solution to optimal control problems for constrained discrete-time linear hybrid systems based on quadratic or linear performance criteria. The aim of the paper it twofold. First we give basic theoretical results on the structure of the optimal state feedback solution and of the value function. Second we describe how the state feedback optimal control law can be effic...

Abstract The problem of linear-quadratic optimal terminal control a linear discrete dynamic system with vector input is considered. Solutions the based on apparatus optimization form pseudo-circulation matrices are given. solution obtained, which ensures achievement goal and passage trajectory as close possible to specified intermediate points. A complete set solutions bundle trajectories obtai...

We study a class of time–domain decomposition based methods for the solution of distributed linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the distributed linear quadratic optimal control problem as a discrete–time optimal control (DTOC) problem in Hilbert space. The optimality conditions for this DTOC problem lead to a linear system wit...

Abstract Balancing a bipedal robot movement against external perturbations is considered challenging and complex topic. This paper discusses how the vibration caused by disturbance has been tackled Linear Quadratic Regulator, which aims to provide optimal control system. A simulation was conducted on MATLAB in order prove concept. Results have shown that linear quadratic regulator successful st...

In this paper, we treat stochastic optimal control problems that are nonlinear in the state, but otherwise are a Linear-Quadratic-Gaussian-Poisson problem in the control (LQGP/U), such that the dynamics are linear in the control with quadratic costs in control. The uncertainty in the environment is modeled by Gaussian noise for continuous background uctuations and discrete random jumps by Pois-...

This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods tha...