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We envision the role of control to expand rapidly in two directions. It will impact novel application areas, which have yet to benefit from the power of feedback, and, as an embedded technology, control will extend its reach far beyond the traditional narrow concept to include higher level functions of operation. Our research program is built on this vision. Eventually, these ideas should also radically...
Most processes of practical interest are hybrid in nature, exhibiting both continuous and discrete characteristics. In many cases, the hybrid behaviour is a result of intrinsic physical phenomena that lead to (practically) instantaneous events such as the appearance and disappearance of thermodynamic phases, changes in flow regimes, equipment failures etc. All such events effect qualitative changes...
One of the most pervasive applications of computing is information processing tightly integrated with physical processes. Embedded computing rapidly takes over the role of being a universal integrator for physical systems. This trend is based on a fundamental technical reason: digital information processing is uniquely suitable for controlling and implementing complex interactions among physical system...
Hybrid systems are richly expressive models for a large variety of potential ap- plications. However, being so rich as to include continuous nonlinear dynamical systems, discrete-event systems and other models of computation (unite-state machines and data ow come to mind here), they are not amenable to com- putationally attractive techniques for synthesis and analysis and present hard numerical problems...
An approach to estimation for a class of hybrid discrete-time linear systems using Luenberger observers is presented. The proposed Luenberger observer for such a kind of systems relies on the switching among different gains. Convergence conditions have been found to ensure the stability of the error dynamics and the related gains may be selected by solving a set of linear matrix inequalities (LMIs)...
In a biological cell, cellular functions and the genetic regula- tory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feed- back pathways appear to incorporate switches that result in changes in the dynamic behavior of the cell. This paper describes...
In this paper, we develop a theory of modular design and refinement of hierarchical hybrid systems. In particular, we present compositional trace-based semantics for the language Charon that allows modular specification of interacting hybrid systems. For hierarchical description of the system architecture, Charon supports building complex agents via the operations of instantiation, hiding, and parallel...
We consider an optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortest-path problem for a finite directed graph. The directed graph we construct is a refinement of the region automaton due to Alur and Dill. We present an exponential...
Reach set computations are of fundamental importance in control theory. We consider the reach set problem for open-loop systems described by parametric inhomogeneous linear differential systems and use real quantifier elimination methods to get exact and approximate solutions. The method employs a reduction of the forward and backward reach set and control parameter set problems to the transcendental...
In this work we present a novel control design methodology for under-actuated mechanical systems. As part of the design process we use the reachability analysis tool d/dt [ABDM99,D00] to see whether there is a switching sequence which can drive the system to a desired periodic orbit. Much of the work in the design of the control law is done manually using classical control techniques (unlike the fully-automatic...
In this paper we develop an algorithm for solving the reachability problem of two-dimensional piece-wise rectangular differential inclusions. Our procedure is not based on the computation of the reach-set but rather on the computation of the limit of individual trajectories. A key idea is the use of one-dimensional affne Poincaré maps for which we can easily compute the fixpoints. As a first step,...
The behavior of the run of an impulse differential inclusion, and, in particular, of a hybrid control system, is “summarized” by the “initialization map” associating with each initial condition the set of new initialized conditions and more generally, by its “substratum”, that is a set-valued map associating with a cadence and a state the next reinitialized state. These maps are characterized in several...
Path-dependent impulse differential inclusions, and in particular, path-dependent hybrid control systems, are defined by a path-dependent differential inclusion (or path-dependent control system, or differential inclusion and control systems with memory) and a path-dependent reset map. In this paper, we characterize the viability property of a closed subset of paths under an impulse path-dependent...
In this paper, we consider the problem of stabilizing the kinematic model of a car to a general path in the plane, subject to very mild restrictions. The car model, although rather simplified, contains some of the most relevant limitations that make application of existing results in the literature impossible: namely, the car can only move forward, and turn with a bounded steering radius; also, only...
This paper introduces the model of linearly priced timed automata as an extension of timed automata, with prices on both transitions and locations. For this model we consider the minimum-cost reachability problem: i.e. given a linearly priced timed automaton and a target state, determine the minimum cost of executions from the initial state to the target state. This problem generalizes the minimum-time...
In this paper we describe a hybrid model and an optimization-based control strategy for solving a traction control prob- lem currently under investigation at Ford Research Laboratories. We show through simulations on a model and a realistic set of parameters that good and robust performance is achieved. Furthermore, the result- ing optimal controller is a piecewise linear function of the measurements...
We consider the synthesis of optimal controls for continuous feedback systems by recasting the problem to a hybrid optimal control problem which is to synthesize optimal enabling conditions for switching between locations in which the control is constant. We provide a single- pass algorithm to solve the dynamic programming problem that arises, with added constraints to ensure non-Zeno trajectories.
In this paper we investigate some analysis and control problems for discrete-time hybrid systems in the piece-wise affine form. By using arguments from the dissipativity theory for nonlinear systems, we show that H∞ analysis and synthesis problems can be formulated and solved via Linear Matrix Inequalities by taking into account the switching structure of the considered system. In this paper we address...
It has been observed that there are a variety of situations in which the most popular hybrid simulation methods can fail to properly detect the occurrence of discrete events. In this paper, we present a method for detecting discrete which, using techniques borrowed from control theory, selects integration step sizes in such a way that the simulation slows down as the state approaches a set which triggers...
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