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Solving parabolic optimal control problems can be inherently challenging in the field of science and engineering, especially with constraints on the nonsmooth distributed control. Motivated by the extensive applicability of the alternating…
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
Closed-loop optimal control design for high-dimensional nonlinear systems has been a long-standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi-Bellman equation, suffer from the curse of dimensionality.…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
A novel robust nonlinear model predictive control strategy is proposed for systems with nonlinear dynamics and convex state and control constraints. Using a sequential convex approximation approach and a difference of convex functions…
Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
This paper proposes a modular approach that combines the online convex optimization framework and reference governors to solve a constrained control problem featuring time-varying and a priori unknown cost functions. Compared to existing…
Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their…
This paper proposes a non-adaptive control solution framework to the practical output regulation problem (PORP) for a class of nonlinear systems with uncertain parameters, unknown control directions and uncertain exosystem dynamics. The…
We consider trajectory optimal control problems in which parameter uncertainty limits the applicability of control trajectories computed prior to travel. Hence, efficient trajectory adjustment is needed to ensure successful travel. However,…
We propose a Model Predictive Control (MPC) with a single-step prediction horizon to approximate the solution of infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems.…
This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we…
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…
In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization,…
By transforming identification and control for nonlinear system into optimization problems, a novel optimization method named state transition algorithm (STA) is introduced to solve the problems. In the proposed STA, a solution to a…
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…
Recently there has been an increasing interest in primal-dual methods for model predictive control (MPC), which require minimizing the (augmented) Lagrangian at each iteration. We propose a novel first order primal-dual method, termed…
Real-time optimization problems are ubiquitous in control and estimation, and are typically parameterized by incoming measurement data and/or operator commands. This paper proposes solving parameterized constrained nonlinear programs using…
Many real-world problems require to optimise trajectories under constraints. Classical approaches are based on optimal control methods but require an exact knowledge of the underlying dynamics, which could be challenging or even out of…