In this paper we present a convex formulation of the Model Predictive Control (MPC) optimisation for energy management in hybrid electric vehicles, and an Alternating Direction Method of Multipliers (ADMM) algorithm for its solution. We develop a new proof of convexity for the problem that allows the nonlinear dynamics to be modelled as a linear system, then demonstrate the performance of ADMM in comparison with Dynamic Programming (DP) through simulation. The results demonstrate up to two orders of magnitude improvement in solution time for comparable accuracy against DP.
In this paper we demonstrate a novel alternating direction method of multipliers (ADMM) algorithm for the solution of the hybrid vehicle energy management problem considering both power split and engine on/off decisions. The solution of a convex relaxation of the problem is used to initialize the optimization, which is necessarily nonconvex, and whilst only local convergence can be guaranteed, it is demonstrated that the algorithm will terminate with the optimal power split for the given engine switching sequence. The algorithm is compared in simulation against a charge-depleting/charge-sustaining (CDCS) strategy and dynamic programming (DP) using real world driver behaviour data, and it is demonstrated that the algorithm achieves 90% of the fuel savings obtained using DP with a 3000fold reduction in computational time.Index Terms-alternating direction method of multipliers, automotive control, energy management, optimization algorithms.
This paper proposes a receding horizon optimization strategy for the problem of energy management in plugin hybrid electric vehicles. The approach employs a dual loop Model Predictive Control (MPC) strategy. An inner feedback loop addresses the problem of optimally tracking a given reference trajectory for the battery state of energy over a short future horizon using knowledge of the predicted driving cycle. An outer feedback loop generates the battery state of energy reference trajectory by solving approximately the optimal energy management problem for the entire driving cycle. The receding horizon optimization problems associated with both inner and outer loops are solved using a specialized projected Newton method. The controller is compared with existing approaches based on Pontryagin's Minimum Principle and the effects of imprecise knowledge of the future driving cycle are discussed. The paper contains a detailed simulation study: first, this assesses the optimality of the associated uncertainty-free approach and its computational load. Secondly, the effects of imprecise knowledge of the future driving cycle are illustrated.
This paper details an investigation into the computational performance of algorithms used for solving a convex formulation of the optimization problem associated with model predictive control for energy management in hybrid electric vehicles with nonlinear losses. A projected interior point method is proposed, where the size and complexity of the Newton step matrix inversion is reduced by applying inequality constraints on the control input as a projection, and its properties are demonstrated through simulation in comparison with an alternating direction method of multipliers (ADMM) algorithm, and general purpose convex optimization software CVX. It is found that the ADMM algorithm has favourable properties when a solution with modest accuracy is required, whereas the projected interior point method is favourable when high accuracy is required, and that both are significantly faster than CVX.Index Terms-alternating direction method of multipliers, energy management, interior point method, model predictive control, plug-in hybrid electric vehicles.
In this paper we propose an Alternating Direction Method of Multipliers (ADMM) algorithm for solving a Model Predictive Control (MPC) optimization problem, in which the system has state and input constraints and a nonlinear input map. The resulting optimization is nonconvex, and we provide a proof of convergence to a point satisfying necessary conditions for optimality. This general method is proposed as a solution for blended mode control of hybrid electric vehicles, to allow optimization in real time. To demonstrate the properties of the algorithm we conduct numerical experiments on randomly generated problems, and show that the algorithm is effective for achieving an approximate solution, but has limitations when an exact solution is required.
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