Identification of task model using piecewise affine systems with variable switching points and its application

The main contribution of this paper is to present the systematic and low-complexity translation techniques between a class of hybrid systems referred to as automaton-based DHA and piecewise affine (PWA) systems. As an starting point the general modeling framework of the automaton-based DHA is represented which models the controlled and uncontrolled switching phenomena between linear continuous dynamics including discrete and continuous states, inputs and outputs. The basic theoretical definitions on the state trajectories of the proposed DHA with forward and backward evolutions which yield forward and backward piecewise affine (FPWA and BPWA) systems are given. Next, the well-posedness and equivalency properties are proposed and the sufficient conditions under which the well-posedness property is achieved with the automaton-based DHA and PWA systems are given. It is shown that the graphical structure of the proposed automaton-based DHA makes it possible to obtain analytically the equivalent PWA system with a polynomial complexity in contrast to the existing numerical translation techniques via decomposed structure of the DHA with an exponential complexity. Examples are presented to confirm the effectiveness of the proposed translation techniques.

This paper proposes an effective control system for a container crane that takes into account disturbances such as a wind. For efficient crane operation, it is necessary to realize accurate positioning of cranes, to minimize oscillation of containers and to realize the fastest possible control time while they are being carried. The crane input is assumed to be a binary with maximum and minimum values for quick control. The entire crane system including the binary input is considered as a hybrid system. A hybrid system is a generic term for a system in which continuous and discrete dynamics exist together. We control the entire crane system using the Mixed Logical Dynamical (MLD) system. An MLD system, which is a representation method for a hybrid system, is used for the crane system. It is generally known that an MLD system can be controlled by Model Predictive Control (MPC). We confirm the effectiveness of the proposed technique through computer simulation of the crane.

We establish equivalences among five classes of hybrid systems, that we have encountered in previous research: mixed logical dynamical systems, linear complementarity systems, extended linear complementarity systems, piecewise affine systems, and max-min-plus-scaling systems. These results are of paramount importance for transferring properties and tools from one class to another.

This paper presents a computational framework for modeling hybrid systems in discrete-time. We introduce the class of discrete hybrid automata (DHA) and show its relation with several other existing model paradigms: piecewise affine systems, mixed logical dynamical systems, (extended) linear complementarity systems, min-max-plus-scaling systems. We present HYSDEL (hybrid systems description language), a high-level modeling language for DHA, and a set of tools for translating DHA into any of the former hybrid models. Such a multimodeling capability of HYSDEL is particularly appealing for exploiting a large number of available analysis and synthesis techniques, each one developed for a particular class of hybrid models. An automotive example shows the modeling capabilities of HYSDEL and how the different models allow to use several computational tools.

Piecewise affine (PWA) systems are autonomous systems with discontinuous vector fields which are affine ordinary differential equations at the points of continuity. These systems have applications to many fields of engineering, including systems biology and traffic engineering. We define what it means for a PWA system to be monotone, and we provide a set of sufficient conditions for monotonicity of PWA systems with hyperrectangular invariants. Such sufficient conditions are useful for understanding the dynamics of such PWA systems and for designing controllers for qualitative, reference tracking. We apply these results towards the drug-discovery problem for the cancer-related p53 pathway.

This paper addresses model reduction for discrete time hybrid systems that are described by a Mixed Logical Dynamical (MLD) model. The goal is to simplify the MLD model while preserving its input/output behavior. This is useful when considering a reachability property that depends on the output and should be enforced by appropriately setting the input. The proposed procedure for model reduction rests on the analysis of the structure of the MLD system and on its observability properties. It is also applicable to PieceWise Affine (PWA) systems that can be equivalently represented as MLD systems. In the case of PWA systems, mode merging can be adopted to further simplify the model.

For linear hybrid systems consisting of linear dynamic equations interacting with linear threshold events, automata, and logic propositions, provided in mixed-logical dynamical (MLD) form, this paper describes an efficient technique for transforming such systems into an equivalent piecewise affine (PWA) form, where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical.

We prove, in a constructive way, the equivalence between hybrid and piecewise affine systems. By focusing our investigation on the latter class, we show through counter-examples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems. Instead, we propose practical numerical tests based on mixed-integer linear programming.

Sequences of Discrete Abstractions for Piecewise Affine Systems

This article is concerned with the adaptive fault‐tolerant tracking control (FTTC) issue with performance constraint for piecewise affine (PWA) systems subject to actuator failures. The mode switching of PWA systems bring out a challenge to guarantee the predefined performance. To conquer this obstacle, a novel adaptive FTTC strategy with time‐varying performance guarantees for PWA systems is devised. First, a piecewise generalized restricted potential function for PWA systems is introduced. Then, by using tracking error, the performance function and a set of matrices, an adaptive FTTC scheme is developed. With the aid of a time‐varying positive definite Lyapunov function, it is proved that the tracking error can be constrained within predefined performance bounds by the developed method. Finally, the simulation results further illustrate the proposed theoretical findings.

This paper addresses system identification of a switched system in which each sub-system is expressed by a piecewise affine system. A considered system is expressed by a mixed logical dynamical system for which some design methods have been already known. For identification, in most cases, a number of sub-systems, that is, switching points are given in advance. However, it is not easy to find switching points for multi-variable systems. Therefore, in this paper, we propose a simultaneous identification technique which takes into account a number of sub-systems and parameters of them. The proposed method is applied to several examples to show its effectiveness.

This paper addresses the design of a fault detection and reconfigurable control structure for bimodal piecewise affine (PWA) systems. The PWA bimodal system will be designed to verify input-to-state stability (ISS) in closed loop. The proposed methodology is divided into two parts. First, a Luenberger-based observer structure is proposed to solve the fault detection and identification (FDI) problem for bimodal PWA systems. The unknown value of the fault parameter is estimated by an observer equation, which is derived using a Lyapunov-based methodology. Then, the ISS property is proved for the observer. Second, a fault-tolerant state feedback controller is synthesized for the PWA model. The controller is designed to deal with partial loss of control authority identified by the observer. The ISS property is also proved for the controller. Finally, the ISS property for the interconnection of the controller and the observer-based fault identification mechanism is studied. The design procedure is formulated as a set of linear matrix inequalities (LMIs), which can be solved efficiently using available software packages.

A duality-based convex optimization approach to L 2 -gain control of piecewise affine slab differential inclusions

The main technological barrier in the commercialization of fuel cells lies in the difficulty of on-board hydrogen storage, especially for portable applications. The technology adopted in this paper to overcome this drawback is to store hydrogen indirectly, in a hydrocarbon form. The stored hydrocarbon fuel can be converted to a hydrogen-rich stream utilizing an autothermal reformer. Pure hydrogen gas can be separated from the gas mixtures exiting the reformer by passing it through a palladium membrane-based gas separation unit. The purified hydrogen gas can be fed to the fuel cell anode and air to the cathode to generate power. A battery unit is considered that serves as a supplementary power source to assist the fuel cell to deliver delay free power, in the presence of uncertainties in the external load. This work basically focuses on the dynamic mathematical modeling and advanced, optimization based control of the integrated reformer–membrane–fuel cell–battery hybrid power system. This work is an extension to an earlier work, where dynamic analysis and basic control studies of the integrated system without a battery unit, were examined. This paper includes a battery unit along with the fuel cell in order to meet the power demand, especially during sudden load fluctuations and plant startup. The presence of two energy sources to control the uncertainty in demand leads to the formation of a mixed logical dynamical (MLD) system. The control of such a MLD system has been attempted in a model predictive control (MPC) framework in this paper. This resulting advanced control scheme has been implemented on the hybrid system to analyze the performance for a representative power application.

The inverted pendulum is the most popular benchmark for teaching and researches in control theory and robotics. Modeling and control of inverted pendulum on a cart is as one of the most important case in control theory. In this paper a new method in Piecewise Affine (PWA) models identification based on numerical analysis is proposed. The evaluation of this algorithm is investigated on a real system. Also the PWA-FUZZY approach as a solution to obviate the problem of hard switching in PWA system is used. A patched LQR and LQG controller in order to stabilize open-loop unstable equilibrium point of this system is proposed.