Ilya V. Kolmanovsky

Theory and computation of disturbance invariant sets for discrete-time linear systems

This paper considers the characterization and computation of invariant sets for discrete-time, time-invariant, linear systems with disturbance inputs whose values are confined to a specified compact set but are otherwise unknown. The emphasis is on determining maximal disturbance-invariant sets X that belong to a specified subset Γ of the state space. Such d-invariant sets have important applications in control problems where there are pointwise-in-time state constraints of the form χ(t)∈Γ . One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic-based, nonlinear multimode regulator. For plants with disturbance inputs and state-control constraints it enlarges the constraint-admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.

MPC-Based Energy Management of a Power-Split Hybrid Electric Vehicle

A power-split hybrid electric vehicle (HEV) combines the advantages of both series and parallel hybrid vehicle architectures by utilizing a planetary gear set to split and combine the power produced by electric machines and a combustion engine. Because of the different modes of operation, devising a near optimal energy management strategy is quite challenging and essential for these vehicles. To improve the fuel economy of a power-split HEV, we first formulate the energy management problem as a nonlinear and constrained optimal control problem. Then two different cost functions are defined and model predictive control (MPC) strategies are utilized to obtain the power split between the combustion engine and electrical machines and the system operating points at each sample time. Simulation results on a closed-loop high-fidelity model of a power-split HEV over multiple standard drive cycles and with different controllers are presented. The results of a nonlinear MPC strategy show a noticeable improvement in fuel economy with respect to those of an available controller in the commercial Powertrain System Analysis Toolkit (PSAT) software and the other proposed methodology by the authors based on a linear time-varying MPC.

Maximal output admissible sets for discrete-time systems with disturbance inputs

The paper considers discrete-time linear systems with constrained disturbance inputs, w(t)/spl isin/Y/spl sub/R/sup m/, t/spl isin/Z/sup +/, and constrained outputs, y(t)/spl isin/Y/spl sub/R/sup p/, t/spl isin/Z/sup +/. An initial state of the system, x(0)/spl isin/R/sup n/, is output admissible if the output constraint is satisfied for all inputs meeting the input constraint; the set of all such states is the maximal output admissible set, O/sub /spl infin//. It is shown that O/sub /spl infin// has basic properties that are similar to those which apply in the disturbance-free case. Procedures for computing O/sub /spl infin// when Y is a polyhedron are available. The set O/sub /spl infin// has important applications, including the determination of regions of attraction for linear closed-loop systems with actuator saturation.

Stochastic MPC With Learning for Driver-Predictive Vehicle Control and its Application to HEV Energy Management

This paper develops an approach for driver-aware vehicle control based on stochastic model predictive control with learning (SMPCL). The framework combines the on-board learning of a Markov chain that represents the driver behavior, a scenario-based approach for stochastic optimization, and quadratic programming. By using quadratic programming, SMPCL can handle, in general, larger state dimension models than stochastic dynamic programming, and can reconfigure in real-time for accommodating changes in driver behavior. The SMPCL approach is demonstrated in the energy management of a series hybrid electrical vehicle, aimed at improving fuel efficiency while enforcing constraints on battery state of charge and power. The SMPCL controller allocates the power from the battery and the engine to meet the driver power request. A Markov chain that models the power request dynamics is learned in real-time to improve the prediction capabilities of model predictive control (MPC). Because of exploiting the learned pattern of the driver behavior, the proposed approach outperforms conventional model predictive control and shows performance close to MPC with full knowledge of future driver power request in standard and real-world driving cycles.

Load governor for fuel cell oxygen starvation protection: a robust nonlinear reference governor approach

The fuel cell oxygen starvation problem is addressed in this paper using a robust load governor. By regulating the current drawn from the fuel cell, the pointwise-in-time constraints on the oxygen excess ratio and on the oxygen mass inside the cathode are strictly enforced to protect the fuel cells from oxygen starvation. The load governor is designed using a nonlinear reference governor approach. Parameter uncertainties such as those due to imperfect controls of temperature and humidity are handled in the load governor design using a novel approach based on sensitivity functions. Simulation results are included to demonstrate the effectiveness of the proposed scheme. The results are compared with those of a linear filter which has been proposed in the prior literature to achieve similar goals.

A stochastic model predictive control approach for series hybrid electric vehicle power management

This paper illustrates the use of stochastic model predictive control (SMPC) for power management in vehicles equipped with advanced hybrid powertrains. Hybrid vehicles use two or more distinct power sources for propulsion, and their complex powertrain architecture requires the coordination of all the subsystems to achieve target performances in terms of fuel consumption, driveability, component life-time, exhaust emissions. Many control strategies have been presented and successfully applied, mainly based on heuristics or rules and tuned on certain reference drive cycles. To take into account that cycles are not exactly known a priori in driving routine, this paper proposes a stochastic approach for the power management problem. We focus on a series hybrid electric vehicle (HEV), which combines an internal combustion engine and an electric motor. The power demand from the driver is modeled as a Markov chain estimated on several driving cycles and used to generate scenarios in the SMPC law. Simulation results over a standard driving cycle are presented to demonstrate the effectiveness of the proposed stochastic approach and compared with other deterministic approaches.

Hybrid feedback laws for a class of cascade nonlinear control systems

A stabilization problem for a class of nonlinear control systems is considered. Systems in this class can be viewed as a cascade connection of a linear time-invariant subsystem, a nonlinear time-periodic static subsystem, and an integrator. Hybrid logic-based feedback controllers are constructed to globally stabilize these systems to the origin. The controllers operate by switching between various time-periodic control functions at discrete-time instants. As specific applications, we consider stabilization of nonholonomic control systems in power form to the origin and stabilization of trajectories for a class of nonlinear control systems. Numerical examples of global stabilization and tracking are reported.

Model Predictive Idle Speed Control: Design, Analysis, and Experimental Evaluation

Idle speed control is a landmark application of feedback control in automotive vehicles that continues to be of significant interest to automotive industry practitioners, since improved idle performance and robustness translate into better fuel economy, emissions and drivability. In this paper, we develop a model predictive control (MPC) strategy for regulating the engine speed to the idle speed set-point by actuating the electronic throttle and the spark timing. The MPC controller coordinates the two actuators according to a specified cost function, while explicitly taking into account constraints on the control and requirements on the acceptable engine speed range, e.g., to avoid engine stalls. Following a process proposed here for the implementation of MPC in automotive applications, an MPC controller is obtained with excellent performance and robustness as demonstrated in actual vehicle tests. In particular, the MPC controller performs better than an existing baseline controller in the vehicle, is robust to changes in operating conditions, and to different types of disturbances. It is also shown that the MPC computational complexity is well within the capability of production electronic control unit and that the improved performance achieved by the MPC controller can translate into fuel economy improvements.

Ultracapacitor Assisted Powertrains: Modeling, Control, Sizing, and the Impact on Fuel Economy

This paper considers modeling and energy management control problems for an automotive powertrain augmented with an ultracapacitor and an induction motor. The ultracapacitor-supplied motor assists the engine during periods of high power demand. The ultracapacitor may be recharged via regeneration during braking and by the engine during periods of low power demand. A reduced-order model and a detailed simulation model of the powertrain are created for control design and evaluation of fuel economy, respectively. A heuristic rule-based controller is used for testing the impact of different component combinations on fuel economy. After a suitable combination of engine, motor, and ultracapacitor sizes has been determined, a model predictive control strategy is created for power management which achieves better fuel economy than the rule-based approach. Various component sizing and control strategies tested consistently indicate a potential for 5% to 15% improvement in fuel economy in city driving with the proposed mild hybrid powertrain. This order of improvement to fuel economy was confirmed by deterministic dynamic programming which finds the best possible fuel economy.

The development of Model Predictive Control in automotive industry: A survey

Model Predictive Control (MPC) is an established control technique in chemical process control, due to its capability of optimally controlling multivariable systems with constraints on plant and actuators. In recent years, the advances in MPC algorithms and design processes, the increased computational power of electronic control units, and the need for improved performance, safety and reduced emissions, have drawn considerable interest in MPC from the automotive industry. In this paper we survey the investigations of MPC in the automotive industry with particular focus on the developments at Ford Motor Company. First, we describe the basic MPC techniques used in the automotive industry, and the early exploratory investigations. Then we present three applications that have been recently prototyped in fully functional production-like vehicles, highlighting the features that make MPC a good candidate strategy for each case. We finally present our perspectives on the next challenges and future applications of MPC in the automotive industry.