Hybrid Optimal Control Theory Research Articles

The minimum principle of hybrid optimal control theory

The minimum principle of hybrid optimal control theory

Modeling air conditioning system with storage evaporator for vehicle energy management

Automotive Air Conditioning (A/C) system significantly affects fuel consumption and emission. Thus, Phase Change Material (PCM) is exploited in an innovative storage evaporator to improve the A/C system performance. Due to hybrid features introduced by mode switching when PCM changes its status between liquid and solid, the task of control-oriented modeling is particularly challenging. Upon the energy-based model built, an optimal control problem of an advanced A/C system with a storage evaporator is formulated as to find an optimal clutch command sequence balancing fuel consumption, cabin comfort and drivability constraints. In the scope of vehicle energy management, Dynamic Programming (DP) algorithm usually serves as a tool of obtaining benchmark optimal solution, against which results from other optimal algorithms are compared. However, a direct application of DP algorithm to the optimal control problem faces unexpected difficulty, because the discretization of state space is not feasible for an irregular multi-dimensional subspace formed by the multi-mode model. Alternatively, hybrid optimal control theory is pursued and a preliminary study is conducted to illustrate its promising application.

Optimal planning of LEO active debris removal based on hybrid optimal control theory

The mission planning of Low Earth Orbit (LEO) active debris removal problem is studied in this paper. Specifically, the Servicing Spacecraft (SSc) and several debris exist on near-circular near-coplanar LEOs. The SSc should repeatedly rendezvous with the debris, and de-orbit them until all debris are removed. Considering the long-duration effect of J2 perturbation, a linear dynamics model is used for each rendezvous. The purpose of this paper is to find the optimal service sequence and rendezvous path with minimum total rendezvous cost (Δv) for the whole mission, and some complex constraints (communication time window constraint, terminal state constraint, and time distribution constraint) should be satisfied meanwhile. Considering this mission as a hybrid optimal control problem, a mathematical model is proposed, as well as the solution method. The proposed approach is demonstrated by a typical active debris removal problem. Numerical experiments show that (1) the model and solution method proposed in this paper can effectively address the planning problem of LEO debris removal; (2) the communication time window constraint and the J2 perturbation have considerable influences on the optimization results; and (3) under the same configuration, some suboptimal sequences are equivalent to the optimal one since their difference in Δv cost is very small.

Optimal scheduling of GEO debris removing based on hybrid optimal control theory

The scheduling of debris removing in a coplanar GEO orbit is studied in this paper. Specifically, the servicing spacecraft is considered to be initially on the circular orbit of the debris to be removed, and it should rendezvous with each debris, remove them to the graveyard orbit and finally return to its initial location. The minimum-cost, two-impulse phasing maneuver is used for each rendezvous. The objective is to find the best sequence with the minimum total Δv to service all debris in the constellation. Considering this mission as a hybrid optimal control problem, a mathematical model is proposed. Based on the analysis and numerous experiments, two heuristic laws of the problem are found out: (1) when targets are sparsely distributed (i.e. each phase angle between the targets is larger than certain threshold), the optimal sequence is the counter-orbit-wise one starting from either the closest leading or the closest lagging target; (2) in general cases, the optimal sequence is the combination of the counter-orbit-wise segments in which each phase angle is larger than a threshold. Then a Rapid Method (RM) is presented based on these laws. It can be concluded from the experiments that the RM is effective and efficient in dealing with this problem especially for the cases with numerous targets.

Calibration of Parallel Hybrid Vehicles Based on Hybrid Optimal Control Theory

Abstract Most energy management systems for hybrid electric vehicles rely on information stored in lookup tables, to define the current mode of operation under certain circumstances. In this paper it is demonstrated how the theory of hybrid optimal control can be used to calculate an initial parameter set for the calibration of parallel hybrid electric vehicles. After solving a hybrid optimal control problem for the fuel optimal operation of the vehicle, taking into account continuous as well as discrete dynamics, the results can be used to automatically calculate lookup tables for optimal gear shifts, optimal torque-split between motor/generator and internal combustion engine and the determination of the drive mode (electric or hybrid mode). The algorithms proposed are easy in their application and can be used for other hybrid vehicle configurations as well and therefore constitute a valuable tool for the initial calibration.

MPC of Switching in a Boost Converter Using a Hybrid State Model With a Sliding Mode Observer

In this paper, a model of a DC-DC (boost) converter is first expressed as a hybrid/switched/variable-structure system state model for the purpose of applying recently developed hybrid optimal control theory to control switching in a boost converter. Switching control is achieved by forming the embedded form of the hybrid state model, which enables the derivation of a control that solves for the switching function that minimizes a user-defined performance index. This approach eliminates the need to form average-value models and provides flexibility to balance competing objectives through appropriate weighting of individual terms in the performance index. Since, in practical situations, both the source voltage and the load resistance vary with time in unknown and unmeasurable ways, we introduce a sliding mode observer based on an enlarged state model which allows implicit estimation of the unknown variables. The combined optimal switching control and sliding mode observer are applied to a boost converter in which several nonidealities and losses are represented. The results of time-domain simulation and hardware experiments are used to validate and compare the response of the hybrid optimal control-sliding mode observer to that of a traditional current-mode control strategy.

Hybrid Optimal Control Framework for Mission Planning

With the progressive sophistication of future missions, it has become increasingly apparent that a new framework is necessary for efficient planning, analysis, and optimization of various concepts of operations (CONOPS). In recognizing that CONOPS involve categorical variables, we propose a hybrid optimal control framework that mathematically formalizes such problems. Hybrid optimal control theory extends ordinary optimal control theory by including categorical variables in the problem formulation. The proposed formalism frees mission planners to focus on high-level decision making by automating and optimizing the details of the inner loops. The eventual goal of this formalism is to develop efficient tools and techniques to support the objective of increasing autonomy for future systems. In using the pseudospectral knotting method to solve hybrid optimal control problems, we generate a mixed-variable programming (MVP) problem. A simple, feasible integer programming subproblem is identified that reduces the combinatorial complexity of solving the MVP. In addition to developing the framework using various examples from aerospace engineering, we provide details for a two-agent benchmark problem associated with a multiagent launch system. The entire process is illustrated with a numerical example.

HEV MODELING FOR A SUPERVISORY LEVEL POWER FLOW CONTROL PROBLEM

This paper explores the modeling equations underlying a supervisory level power flow control problem for a hybrid electric vehicle (HEV). For a given driving profile, a supervisory controller decides on the power split between the ICE and the battery-electric-motor-generator to achieve optimal performance, e.g., a trade-off between energy usage, driving profile tracking, and drivability constraints. Formulation and solution of such a problem require a supervisory level power flow control model amenable to hybrid optimal control techniques. This paper develops constrained power flow control models for the various HEV subsystems and their interactions, along with a differential equation modeling the HEV's longitudinal dynamics amenable to recent advances in hybrid optimal control theory.