Strong Stationarity Conditions for Optimal Control of Hybrid Systems

We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush-Kuhn-Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality. We proceed to show that the dynamics of every continuous piecewise affine system can be written as the optimizer of a mathematical program which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with piecewise affine dynamics. We present simulation results showing the substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation.Comment: 30 pages, 4 figure

Analysis of the explicit model predictive control for semi-active suspension

Explicit model predictive control (MPC) enhances application of MPC to areas where the fast online computation of the control signal is crucial, such as in aircraft or vehicle control. Explicit MPC controllers consist of several affine feedback gains, each of them valid over a polyhedral region of the state space. In this paper the optimal control of the quarter car semi-active suspension is studied. After a detailed theoretical introduction to the modeling, clipped LQ control and explicit MPC, the article demonstrates that there may exist regions where constrained MPC/explicit MPC has no feasible solution. To overcome this problem the use of soft constraints and combined clipped LQ/MPC methods are suggested. The paper also shows that the clipped optimal LQ solution equals to the MPC with horizon N=1 for the whole union of explicit MPC regions. We study the explicit MPC of the semi-active suspension with actual discrete time observer connected to the explicit MPC in order to increase its practical applicabili ty. The controller requires only measurement of the suspension deflection. Performance of the derived controller is evaluated through simulations where shock tests and white noise velocity disturbances are applied to a real quarter car vertical model. Comparing MPC and the clipped LQ approach, no essential improvement was detected in the control behavior

PHM Basado en Modelo Híbrido para Sistema Supervisor Utilizando Labview

Este trabajo está motivado por la creciente dependencia de la sociedad moderna de los sistemas autónomos y procesos tecnológicos complejos, donde disponibilidad, fiabilidad y seguridad son palabras estratégicas en la alta competencia industrial. Para cumplir estos requisitos el mantenimiento se convierte en parte imprescindible. En el mundo industrial el coste de mantenimiento es una parte importante del total de los costos operativos y una parte fundamental para que los sistemas funcionen correctamente, con la creciente demanda de un buen mantenimiento. Por este motivo se presenta un estudio de metodologías que permitan predecir las condiciones de funcionamiento de los componentes del sistema, dichas metodologías se basan en sistemas híbridos y redes neuronales en asociación con estrategias de predicción, capaces de predecir el estado futuro del conjunto. En este estudio se presenta un método de Prognosis and Health Management, donde los datos utilizados para caracterizar el modelo híbrido provienen de un sistema real, en el cual se han instalado diversos sensores analógicos y digitales para extraer sus características de funcionamiento. Se ha utilizado un sistema de adquisición basado en LabView mediante el cual es posible recoger las observaciones disponibles en el sistema, y extraer la información necesaria para diseñar modelos de predicción. Los resultado muestran que el modelo de predicción basado en un sistema hibrido puede seguir el estado del sistema y tiene el potencial para ser usado como herramienta de pronostico y diagnostico precoz de fallas. Para la elaboración del trabajo se han utilizado diversas herramientas informáticas, la más importante ha sido LabView, software de National Instruments, y MartixX de la misma compañía, asimismo se ha utilizado MATLAB para las simulaciones, pre-procesado y estudio de datos

Nonlinear predictive restricted structure control

This thesis defines new developments in predictive restricted structure control for industrial applications. It begins by describing the augmented system for both state-space and polynomial model descriptions. These descriptions can contain the plant model, the disturbance model, and any additional essential model subsystems. It then describes the predictive restricted structure control solution for both linear and nonlinear systems in state-space form. The solution utilizes the recent development in nonlinear predictive generalized minimum variance by adding a general operator subsystem that defines nonlinear system along with the linear or the linear parameter varying output subsystem. The next contribution is the polynomial predictive restricted structure control algorithm for polynomial linear parameter varying model that may result from nonlinear equations or experimental data-driven model identification. This algorithm utilizes the generalised predictive control method to approximate and control nonlinear systems in the linear parameter varying system inputoutput transfer operator matrices. The solution is simple in unconstrained and constrained optimization solutions and required a small computing capacity. Four examples have been chosen to test the algorithms for different nonlinear characteristics. In the first three examples, state-space versions of the algorithm for the linear, the quasi-linear parameter varying and the state-dependent were employed to control the quadruple tank process, electronic throttle body, and the continuous stirred tank reactors. In the last example, the polynomial linear parameter varying restricted structure controller is used to control automotive variable camshaft timing system.This thesis defines new developments in predictive restricted structure control for industrial applications. It begins by describing the augmented system for both state-space and polynomial model descriptions. These descriptions can contain the plant model, the disturbance model, and any additional essential model subsystems. It then describes the predictive restricted structure control solution for both linear and nonlinear systems in state-space form. The solution utilizes the recent development in nonlinear predictive generalized minimum variance by adding a general operator subsystem that defines nonlinear system along with the linear or the linear parameter varying output subsystem. The next contribution is the polynomial predictive restricted structure control algorithm for polynomial linear parameter varying model that may result from nonlinear equations or experimental data-driven model identification. This algorithm utilizes the generalised predictive control method to approximate and control nonlinear systems in the linear parameter varying system inputoutput transfer operator matrices. The solution is simple in unconstrained and constrained optimization solutions and required a small computing capacity. Four examples have been chosen to test the algorithms for different nonlinear characteristics. In the first three examples, state-space versions of the algorithm for the linear, the quasi-linear parameter varying and the state-dependent were employed to control the quadruple tank process, electronic throttle body, and the continuous stirred tank reactors. In the last example, the polynomial linear parameter varying restricted structure controller is used to control automotive variable camshaft timing system

Optimal control of a class of linear hybrid systems with saturation

Abstract We consider a class of queueing systems that can operate in several modes; in each mode the queue lengths exhibit a linear growth until a specified upper or lower level is reached, after which the queue length stays at that level until the end of the mode. We present some methods to determine the optimal switching time instants that minimize a criterion such as average queue length, worst case queue length, average waiting time, and so on. We show that if there is no upper saturation then for some objective functions the optimal switching scheme can be computed very efficiently