Related papers: Safe Optimal Control using Log Barrier Constrained…
Designing controllers to generate various trajectories has been studied for years, while recently, recovering an optimal controller from trajectories receives increasing attention. In this paper, we reveal that the inherent linear quadratic…
This paper introduces a receding horizon like control scheme for localizable distributed systems, in which the effect of each local disturbance is limited spatially and temporally. We characterize such systems by a set of linear equality…
For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs.…
This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with constant coefficients. It is proved that the non-emptiness of the admissible control set for all initial state is…
Learning-based control methods for industrial processes leverage the repetitive nature of the underlying process to learn optimal inputs for the system. While many works focus on linear systems, real-world problems involve nonlinear…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
Lane-free vehicle movement has been recently proposed for connected automated vehicles (CAV) due to various potential advantages. One such advantage stems from the fact that incremental changes of the road width in lane-free traffic lead to…
A $\mathcal{H}_2$-guaranteed sparse-feedback linear-quadratic (LQ) optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where $\ell_0$-penalty is added into the $\mathcal{H}_2$ cost to…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
It is well known that highly volatile control laws, while theoretically optimal for certain systems, are undesirable from an engineering perspective, being generally deleterious to the controlled system. In this article we are concerned…
In order to perform highly dynamic and agile maneuvers, legged robots typically spend time in underactuated domains (e.g. with feet off the ground) where the system has limited command of its acceleration and a constrained amount of time…
The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal…
We consider the linear quadratic regulator (LQR) for one-dimensional linear evolution partial differential equations (PDEs) on a finite interval in space. The control is applied as an additive forcing term to PDEs. Existing methods for…
The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a…
The existence of multiple irregular obstacles in the environment introduces nonconvex constraints into the optimization for motion planning, which makes the optimal control problem hard to handle. One efficient approach to address this…
The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the…
Distributional linear quadratic regulator (LQR) is a new framework that integrates the distributional reinforcement learning and classical LQR, which offers a new way to study the random return instead of the expected cost. Unlike iterative…
As it is popular known, Riccati equation is the key basic tool for optimal control in the modern control theory. The solvability conditions of optimal control, stabilization conditions and controller design are all based on the Riccati…
Trajectory optimization is a popular strategy for planning trajectories for robotic systems. However, many robotic tasks require changing contact conditions, which is difficult due to the hybrid nature of the dynamics. The optimal sequence…