Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConstrained stochastic LQ control on infinite time horizon with regime switching
81
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. Two new extended stochastic Riccati equations (ESREs) on infinite time horizon are introduced. The existence of the nonnegative solutions, in both standard and singular cases, is proved through a sequence of ESREs on finite time horizon. Based on this result and some approximation techniques, we obtain the optimal state feedback control and optimal value for the stochastic LQ problem explicitly, which also implies the uniqueness of solutions for the ESREs. Finally, we apply these results to solve a lifetime portfolio selection problem of tracking a given wealth level with regime switching and portfolio constraint.
rate research
Read More
A class of infinite horizon optimal control problems involving mixed quasi-norms of $L^p$-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization.
This paper is devoted to analysing the explicit slow decay rate and turnpike in the infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Assume that some weak observability or controllability are satisfied, by which, the lower and upper bounds of the corresponding algebraic Riccati operator are estimated, respectively. Then based on these two bounds, the explicit slow decay rate of the closed-loop system with Riccati-based optimal feedback control is obtained. The averaged turnpike property for this problem is also further discussed. We then apply these results to the LQ optimal control problems constraint to networks of one-dimensional wave equations and also some multi-dimensional ones with local controls which lack of GCC(Geometric Control Condition).
The behaviour of a stochastic dynamical system may be largely influenced by those low-probability, yet extreme events. To address such occurrences, this paper proposes an infinite-horizon risk-constrained Linear Quadratic Regulator (LQR) framework with time-average cost. In addition to the standard LQR objective, the average one-stage predictive variance of the state penalty is constrained to lie within a user-specified level. By leveraging the duality, its optimal solution is first shown to be stationary and affine in the state, i.e., $u(x,lambda^*) = -K(lambda^*)x + l(lambda^*)$, where $lambda^*$ is an optimal multiplier, used to address the risk constraint. Then, we establish the stability of the resulting closed-loop system. Furthermore, we propose a primal-dual method with sublinear convergence rate to find an optimal policy $u(x,lambda^*)$. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed framework and the primal-dual method.
We use the continuation and bifurcation package pde2path to numerically analyze infinite time horizon optimal control problems for parabolic systems of PDEs. The basic idea is a two step approach to the canonical systems, derived from Pontryagins maximum principle. First we find branches of steady or time-periodic states of the canonical systems, i.e., canonical steady states (CSS) respectively canonical periodic states (CPS), and then use these results to compute time-dependent canonical paths connecting to a CSS or a CPS with the so called saddle point property. This is a (high dimensional) boundary value problem in time, which we solve by a continuation algorithm in the initial states. We first explain the algorithms and then the implementation via some example problems and associated pde2path demo directories. The first two examples deal with the optimal management of a distributed shallow lake, and of a vegetation system, both with (spatially, and temporally) distributed controls. These examples show interesting bifurcations of so called patterned CSS, including patterned optimal steady states. As a third example we discuss optimal boundary control of a fishing problem with boundary catch. For the case of CPS-targets we first focus on an ODE toy model to explain and validate the method, and then discuss an optimal pollution mitigation PDE model.
We present two nonparametric approaches to Kullback-Leibler (KL) control, or linearly-solvable Markov decision problem (LMDP) based on Gaussian processes (GP) and Nystr{o}m approximation. Compared to recently developed parametric methods, the proposed data-driven frameworks feature accurate function approximation and efficient on-line operations. Theoretically, we derive the mathematical connection of KL control based on dynamic programming with earlier work in control theory which relies on information theoretic dualities for the infinite time horizon case. Algorithmically, we give explicit optimal control policies in nonparametric forms, and propose on-line update schemes with budgeted computational costs. Numerical results demonstrate the effectiveness and usefulness of the proposed frameworks.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
