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This paper concerns two algorithms for solving optimal control problems with hybrid systems. The first algorithm aims at hybrid systems exhibiting sliding modes. The first algorithm has several features which distinguishes it from the other…
This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. A sliding mode is coped with differential-algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion…
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the optimal control problem can be solved by gluing together the…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid version of Pontryagin's maximum principle is presented. This…
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
We present a numerically tractable formulation for computing the optimal control of the class of hybrid dynamical systems whose trajectories are continuous. Our formulation, an extension of existing relaxed-control techniques for switched…
The Hybrid Minimum Principle (HMP) is established for the optimal control of deterministic hybrid systems with both autonomous and controlled switchings and jumps where state jumps at the switching instants are permitted to be accompanied…
This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
Model predictive control (MPC) of hybrid dynamical systems is challenging because the associated optimization problem is nonsmooth and the resulting feedback law is discontinuous. This paper develops real-time MPC algorithms for nonlinear…
This work develops a control-centric framework for a custom 4-DOF rigid-body manipulator by coupling a reduced-order Pontryagin's Maximum Principle (PMP) controller with a physics-informed Gradient Descent stage. The reduced PMP model…