Daniele Bernardini

Vehicle Yaw Stability Control by Coordinated Active Front Steering and Differential Braking in the Tire Sideslip Angles Domain

Vehicle active safety receives ever increasing attention in the attempt to achieve zero accidents on the road. In this paper, we investigate a control architecture that has the potential of improving yaw stability control by achieving faster convergence and reduced impact on the longitudinal dynamics. We consider a system where active front steering and differential braking are available and propose a model predictive control (MPC) strategy to coordinate the actuators. We formulate the vehicle dynamics with respect to the tire slip angles and use a piecewise affine (PWA) approximation of the tire force characteristics. The resulting PWA system is used as prediction model in a hybrid MPC strategy. After assessing the benefits of the proposed approach, we synthesize the controller by using a switched MPC strategy, where the tire conditions (linear/saturated) are assumed not to change during the prediction horizon. The assessment of the controller computational load and memory requirements indicates that it is capable of real-time execution in automotive-grade electronic control units. Experimental tests in different maneuvers executed on low-friction surfaces demonstrate the high performance of the controller.

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.

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.

Brief paper: Stability analysis of stochastic networked control systems

In this paper, we study the stability of Networked Control Systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, packet-dropouts and communication constraints. Communication constraints impose that, per transmission, only one sensor or actuator node can access the network and send its information. Which node is given access to the network at a transmission time is orchestrated by a so-called network protocol. This paper considers NCSs, in which the transmission intervals and transmission delays are described by a random process, having a continuous probability density function (PDF). By focussing on linear plants and controllers and periodic and quadratic protocols, we present a modelling framework for NCSs based on stochastic discrete-time switched linear systems. Stability (in the mean-square) of these systems is analysed using convex overapproximations and a finite number of linear matrix inequalities. On a benchmark example of a batch reactor, we illustrated the effectiveness of the developed theory.

Scenario-based model predictive control of stochastic constrained linear systems

In this paper we propose a stochastic model predictive control (MPC) formulation based on scenario generation for linear systems affected by discrete multiplicative disturbances. By separating the problems of (1) stochastic performance, and (2) stochastic stabilization and robust constraints fulfillment of the closed-loop system, we aim at obtaining a less conservative control action with respect to classical robust MPC schemes, still enforcing convergence and feasibility properties for the controlled system. Stochastic performance is addressed for very general classes of stochastic disturbance processes, although discretized in the probability space, by adopting ideas from multi-stage stochastic optimization. Stochastic stability and recursive feasibility are enforced through linear matrix inequality (LMI) problems, which are solved off-line; stochastic performance is optimized by an on-line MPC problem which is formulated as a convex quadratically constrained quadratic program (QCQP) and solved in a receding horizon fashion. The performance achieved by the proposed approach is shown in simulation and compared to the one obtained by standard robust and deterministic MPC schemes.

Stabilizing Model Predictive Control of Stochastic Constrained Linear Systems

This paper investigates stochastic stabilization procedures based on quadratic and piecewise linear Lyapunov functions for discrete-time linear systems affected by multiplicative disturbances and subject to linear constraints on inputs and states. A stochastic model predictive control (SMPC) design approach is proposed to optimize closed-loop performance while enforcing constraints. Conditions for stochastic convergence and robust constraints fulfillment of the closed-loop system are enforced by solving linear matrix inequality problems off line. Performance is optimized on line using multistage stochastic optimization based on enumeration of scenarios, that amounts to solving a quadratic program subject to either quadratic or linear constraints. In the latter case, an explicit form is computable to ease the implementation of the proposed SMPC law. The approach can deal with a very general class of stochastic disturbance processes with discrete probability distribution. The effectiveness of the proposed SMPC formulation is shown on a numerical example and compared to traditional MPC schemes.

Energy-aware robust model predictive control based on noisy wireless sensors

Wireless sensor networks (WSNs) are becoming fundamental components of modern control systems due to their flexibility, ease of deployment and low cost. However, the energy-constrained nature of WSNs poses new issues in control design; in particular the discharge of batteries of sensor nodes, which is mainly due to radio communications, must be taken into account. In this paper we present a novel transmission strategy for communication between controller and sensors which is intended to minimize the data exchange over the wireless channel. Moreover, we propose an energy-aware control technique for constrained linear systems based on explicit model predictive control (MPC), providing closed-loop stability in the presence of disturbances. The presented control schemes are compared to traditional MPC techniques. The results show the effectiveness of the proposed energy-aware approach, which achieves a profitable trade-off between energy savings and closed-loop performance.

Energy-aware robust Model Predictive Control based on wireless sensor feedback

Flexibility, ease of deployment and of spatial reconfiguration, and low cost make wireless sensor networks (WSNs) fundamental component of modern networked control systems. However, due to the energy-constrained nature of WSNs, the transmission rate of the sensor nodes is a critical aspect to take into account in control design. Two are the main contributions of this paper. First, a general transmission strategy for communication between controller and sensors is proposed. Then, a scenario with a controller and a wireless node providing measures is investigated, and two energy-aware control schemes based on explicit model predictive control (MPC) are presented. We consider both nominal and robust control in the presence of disturbances, and convergence properties are given for the latter. The proposed control schemes are tested and compared to traditional MPC techniques. The results show the effectiveness of the proposed energy-aware approach, which achieves a profitable trade-off between energy consumption of wireless sensors and loss in system performance.

Steering Vehicle Control by Switched Model Predictive Control

We propose a switching Model Predictive Control (MPC) strategy to control vehicle steering by actuating active front steering (AFS) and electronic stability control (ESC). After describing the piecewise affine prediction model used for MPC design, where the nonlinearities arise from the relation between sideslip angles and tire forces, a switching MPC strategy is implemented, where different local MPC controllers are used depending on the current tire force conditions. The designed controller maintains most of the benefits of a previously designed hybrid model predictive controller, but it has lower complexity and allows more flexible design. The controller stability is verified and the controller behavior during challenging step steering maneuvers is tested in closed-loop simulations against a nonlinear vehicle model.

Stability and Invariance Analysis of Approximate Explicit MPC Based on PWA Lyapunov Functions

Abstract For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set X, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing X by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set X of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.