This paper considers the problem of computing the non-causal minimum-fuel energy management strategy of a hybrid electric vehicle on a given driving cycle. Specifically, we address the multiphase mixed-integer nonlinear optimal control problem arising when optimal gear choice, torque split and engine on/off controls are sought in off-line evaluations. We propose an efficient model by … Read more
In this work, we introduce a novel numerical algorithm, called RaBVItG (Radial Basis Value Iteration Game) to approximate feedback-Nash equilibria for deterministic differential games. More precisely, RaBVItG is an algorithm based on value iteration schemes in a meshfree context. It is used to approximate optimal feedback Nash policies for multi-players, trying to tackle the dimensionality … Read more
Planning under uncertainty is a frequently encountered problem. Noisy observation is a typical situation that introduces uncertainty. Such a problem can be formulated as a Partially Observable Markov Decision Process (POMDP). However, solving a POMDP is nontrivial and can be computationally expensive in continuous state, action, observation and latent state space. Through this work, we … Read more
This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal … Read more
We consider a direct approach to solve mixed-integer nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach … Read more
In this article, we present a framework for the numerical solution of optimal control problems, constrained by ordinary differential equations which can run in (finitely many) different modes, where a change of modes leads to additional switching cost in the cost function, and whenever the system changes its mode, jumps in the differential states are … Read more
We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. In order to provide numerical convergence guarantees, it is sufficient for the functions that define the problem to satisfy boundedness and Lipschitz conditions. Our assumptions are the most general to date; we do not require uniqueness, differentiability … Read more
We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and con- tinuous time. The set of all invariant measures is characterized as the feasible set of an infinite-dimensional linear program (LP). The objective functional of this LP is then used to single-out a specific measure … Read more
We consider the problem of approximating numerically the moments and the supports of measures which are invariant with respect to the dynamics of continuousand discrete-time polynomial systems, under semialgebraic set constraints. First, we address the problem of approximating the density and hence the support of an invariant measure which is absolutely continuous with respect to … Read more
Within this work, we present a warm-started algorithm for Model Predictive Control (MPC) of switched nonlinear systems under combinatorial constraints based on Combinatorial Integral Approximation (CIA). To facilitate high-speed solutions, we introduce a preprocessing step for complexity reduction of CIA problems, and include this approach within a new toolbox for solution of CIA problems with … Read more