The goal of this paper is to address finite-horizon minimum variance and covariance steering problems for discrete-time stochastic (Gaussian) linear systems. On the one hand, the minimum variance problem seeks for a control policy that will steer the state mean of an uncertain system to a prescribed quantity while minimizing the trace of its terminal state covariance (or variance). On the other hand, the covariance steering problem seeks for a control policy that will steer the covariance of the terminal state to a prescribed positive definite matrix. We propose a solution approach that relies on the stochastic version of the affine disturbance feedback control parametrization according to which the control input at each stage can be expressed as an affine function of the history of disturbances that have acted upon the system. Our analysis reveals that this particular parametrization allows one to reduce the stochastic optimal control problems considered herein into tractable convex programs with essentially the same decision variables. This is in contrast with other control policy parametrizations, such as the state feedback parametrization, in which the decision variables of the convex program do not coincide with the controller's parameters of the stochastic optimal control problem. In addition, we propose a variation of the control parametrization which relies on truncated histories of past disturbances. We show that by selecting the length of the truncated sequences appropriately, we can design suboptimal controllers which can strike the desired balance between performance and computational cost.
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a tractable convex approximation of the optimal covariance steering problem is developed by tightening the chance constraints and by introducing a suitable change of variables. The solution of the convex approximation is shown to be a valid (albeit potentially suboptimal) solution to the original chance-constrained covariance steering problem.
We propose to solve a constrained distribution steering problem, i.e., steering a stochastic linear system from an initial distribution to some final, desired distribution subject to chance constraints. We do so by characterizing the cumulative distribution function in the chance constraints and by using the absolute distance between two probability density functions using the corresponding characteristic functions. We consider discrete-time, time-varying linear systems with affine feedback. We demonstrate the proposed approach on a 2D double-integrator perturbed by various disturbances and in…
The problem of optimizing affine feedback laws that explicitly steer the mean and covariance of an uncertain system state in the presence of a Gaussian random field is considered. Spatially-dependent disturbances are successively approximated with respect to a nominal trajectory by a sequence of jointly Gaussian random vectors. Sequential updates to the nominal control inputs are computed via convex optimization that includes the effect of affine state feedback, the perturbing effects of spatial disturbances, and chance constraints on the closed-loop state and control. The developed method is …
In this paper, we present a new control policy parametrization for the finite-horizon covariance steering problem for discrete-time Gaussian linear systems (DTGLS) which can reduce the latter stochastic optimal control problem to a tractable optimization problem. The covariance steering problem seeks for a feedback control policy that will steer the state covariance of a DTGLS to a desired positive definite matrix in finite time. We consider two different formulations of the covariance steering problem, one with hard terminal LMI constraints (hard-constrained covariance steering) and another o…
In this paper, we present a new trajectory optimization algorithm for stochastic linear systems which combines Model Predictive Path Integral (MPPI) control with Constrained Covariance Steering (CSS) to achieve high performance with safety guarantees (robustness). Although MPPI can be used to solve complex nonlinear trajectory optimization problems, it may not always handle constraints effectively and its performance may degrade in the presence of unmodeled disturbances. By contrast, CCS can handle probabilistic state and / or input constraints (e.g., chance constraints) and also steer the sta…
Robust global stabilization of nonlinear systems by observer-based feedback controllers is a challenging task. This article investigates the problem of designing observer-based stabilizing controllers for incrementally quadratic nonlinear systems with external disturbances. The nonlinearities considered in the system model satisfy the incremental quadratic constraints, which are characterized by incremental multiplier matrices and encompass many common nonlinearities. The simultaneous search for the observer and the controller gain matrices is formulated as a feasibility problem of linear matr…
This work addresses the problem of vehicle path planning in the presence of obstacles and uncertainties, which is a fundamental problem in robotics. While many path planning algorithms have been proposed for decades, many of them have dealt with only deterministic environments or only open-loop uncertainty, i.e., the uncertainty of the system state is not controlled and, typically, increases with time due to exogenous disturbances, which leads to the design of potentially conservative nominal paths. In order to deal with disturbances and reduce uncertainty, generally, a lower-level feedback co…
Optimal Universal Controllers for Roll Stabilization
Oceaneering AGV Systems B.V.（Oceaneering AGV系统有限公司）；University of Groningen（格罗宁根大学）；Politecnico di Torino（都灵理工大学）；Institute for Problems of Mechanical Engineering（机械工程学院问题研究所）
This paper involves the innovative development of a symmetric Gauss-Seidel ADMM algorithm to solve the H-infinity guaranteed cost control problem. In the presence of parametric uncertainties, the H-infinity guaranteed cost control problem generally leads to the large-scale optimization. This is due to the exponential growth of the number of the extreme systems involved with respect to the number of parametric uncertainties. In this work, through a variant of the Youla-Kucera parameterization, the stabilizing controllers are parameterized in a convex set; yielding the outcome that the H-infinit…
This paper addresses the problem of robust control of a linear discrete-time system subject to bounded disturbances and to measurement and control budget constraints. Using Q-parameterization and a polytope containment method, we prove that the co-design of an affine feedback controller, a measurement schedule and a control schedule can be exactly formulated as a mixed integer linear program with 2 binary variables per time step. As a consequence, this problem can be solved efficiently, even when an exhaustive search for measurement and control times would have been impossible in a reasonable …
In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded disturbances, stochastic noise and potentially Markovian switching over a finite horizon. We investigate the situation when performance specifications are expressed via averaged quadratic inequalities on the random state-control trajectory. Our methodology also applies to steering the density of the state-control trajectory under set bounded uncertainty. Our developments are based on expanding the…
Iowa State University（爱荷华州立大学）；Scuola Superiore Meridionale（南方高等学院）；Georgia Institute of Technology（佐治亚理工学院）；University of California Santa Cruz（加州大学圣克鲁兹分校）
The traditional secondary frequency control of power systems restores nominal frequency by steering Area Control Errors (ACEs) to zero. Existing methods are a form of integral control with the characteristic that large control gain coefficients introduce an overshoot and small ones result in a slow convergence to a steady state. In order to deal with the large frequency deviation problem, which is the main concern of the power system integrated with a large number of renewable energy, a faster convergence is critical. In this paper, we propose a secondary frequency control method named Power-I…
Feedback control theory has been extensively implemented to theoretically model human sensorimotor control. However, experimental platforms capable of manipulating important components of multiple feedback loops lack development. This paper describes the WheelCon, which is an open source platform aimed at resolving such insufficiencies. WheelCon enables safely simulation of the canonical sensorimotor task such as riding a mountain bike down a steep, twisting, bumpy trail etc., with provided only a computer, standard display, and an inexpensive gaming steering wheel with a force feedback motor.…
