scholarly journals General Lyapunov-Based Iterative Algorithm for Linear Quadratic Regulator Problem of Stochastic Systems with Markovian Jump

2021 ◽  
Author(s):  
Meijun Liu ◽  
Xueyan Zhao ◽  
feiqi Deng
Keyword(s):  
Stochastic Systems ◽  
Initial Conditions ◽  
Iterative Algorithms ◽  
Linear Quadratic Regulator ◽  
Lyapunov Equation ◽  
Markovian Jump ◽  
Linear Quadratic ◽  
Lqr Problem ◽  
Linear Stochastic Systems ◽  
Monotonic Convergence

This paper investigates the linear quadratic regulator(LQR) problem of linear stochastic systems with Markovian jump. Firstly, two iterative algorithms are proposed for solving the corresponding coupled algebraic Riccati equa- tions (CAREs) based on the general-type Lyapunov equation derived from linear stochastic systems. It is verified that the second algorithm adding an adjustable factor converges faster than the first one without it. Secondly, a monotonic convergence theorem is established for the proposed iterative algorithms under certain initial conditions. In the end, a numerical example is given to verify the efficiency of the proposed algorithms.

scholarly journals General Lyapunov-Based Iterative Algorithm for Linear Quadratic Regulator Problem of Stochastic Systems with Markovian Jump

2021 ◽  
Author(s):  
Meijun Liu ◽  
Xueyan Zhao ◽  
feiqi Deng
Keyword(s):  
Stochastic Systems ◽  
Initial Conditions ◽  
Iterative Algorithms ◽  
Linear Quadratic Regulator ◽  
Lyapunov Equation ◽  
Markovian Jump ◽  
Linear Quadratic ◽  
Lqr Problem ◽  
Linear Stochastic Systems ◽  
Monotonic Convergence

This paper investigates the linear quadratic regulator(LQR) problem of linear stochastic systems with Markovian jump. Firstly, two iterative algorithms are proposed for solving the corresponding coupled algebraic Riccati equa- tions (CAREs) based on the general-type Lyapunov equation derived from linear stochastic systems. It is verified that the second algorithm adding an adjustable factor converges faster than the first one without it. Secondly, a monotonic convergence theorem is established for the proposed iterative algorithms under certain initial conditions. In the end, a numerical example is given to verify the efficiency of the proposed algorithms.

Robust Optimization in Possibility Theory

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Dominik Hose ◽  
Markus Mäck ◽  
Michael Hanss
Keyword(s):  
Decision Making ◽  
Robust Optimization ◽  
Objective Function ◽  
Optimization Problems ◽  
Initial Conditions ◽  
Multicriteria Decision Making ◽  
Possibility Theory ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Multicriteria Decision

Abstract In this contribution, the optimization of systems under uncertainty is considered. The possibilistic evaluation of the fuzzy-valued constraints and the adoption of a multicriteria decision making technique for the fuzzy-valued objective function enable a meaningful solution to general fuzzy-valued optimization problems. The presented approach is universally applicable, which is demonstrated by reformulating and solving the linear quadratic regulator problem for fuzzy-valued system matrices and initial conditions.

scholarly journals Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems

2010 ◽  
Vol 20 (4) ◽  
pp. 655-664 ◽  
Author(s):  
Keyword(s):  
Semidefinite Programming ◽  
Linear Quadratic Regulator ◽  
Descriptor Systems ◽  
Programming Approach ◽  
State Control ◽  
Linear Quadratic ◽  
Control Pair ◽  
Elegant Method ◽  
Lqr Problem ◽  
Primal Dual

Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systemsThis paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant method to solve the problem under consideration. Numerical examples are given to illustrate the results.

scholarly journals iLQR-VAE : control-based learning of input-driven dynamics with applications to neural data

2021 ◽  
Author(s):  
Marine Schimel ◽  
Ta-Chu Kao ◽  
Kristopher T. Jensen ◽  
Guillaume Hennequin
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Linear Quadratic Regulator ◽  
External Input ◽  
Learning Approaches ◽  
Linear Quadratic ◽  
Nonlinear Dynamical ◽  
Neural Data ◽  
Recognition Model ◽  
Variational Autoencoder

Understanding how neural dynamics give rise to behaviour is one of the most fundamental questions in systems neuroscience. To achieve this, a common approach is to record neural populations in behaving animals, and model these data as emanating from a latent dynamical system whose state trajectories can then be related back to behavioural observations via some form of decoding. As recordings are typically performed in localized circuits that form only a part of the wider implicated network, it is important to simultaneously learn the local dynamics and infer any unobserved external input that might drive them. Here, we introduce iLQR-VAE, a novel control-based approach to variational inference in nonlinear dynamical systems, capable of learning both latent dynamics, initial conditions, and ongoing external inputs. As in recent deep learning approaches, our method is based on an input-driven sequential variational autoencoder (VAE). The main novelty lies in the use of the powerful iterative linear quadratic regulator algorithm (iLQR) in the recognition model. Optimization of the standard evidence lower-bound requires differentiating through iLQR solutions, which is made possible by recent advances in differentiable control. Importantly, having the recognition model implicitly defined by the generative model greatly reduces the number of free parameters and allows for flexible, high-quality inference. This makes it possible for instance to evaluate the model on a single long trial after training on smaller chunks. We demonstrate the effectiveness of iLQR-VAE on a range of synthetic systems, with autonomous as well as input-driven dynamics. We further show state-of-the-art performance on neural and behavioural recordings in non-human primates during two different reaching tasks.

Sign in / Sign up

Export Citation Format

Share Document