We study the problem of fitting a piecewise affine (PWA) function to input–output data. Our algorithm divides the input domain into finitely many regions whose shapes are specified by a user-provided template and such that the input–output data in each region are fit by an affine function within a user-provided error tolerance. We first prove that this problem is NP-hard. Then, we present a top-down algorithmic approach for solving the problem. The algorithm considers subsets of the data points in a systematic manner, trying to fit an affine function for each subset using linear regression. If regression fails on a subset, the algorithm extracts a minimal set of points from the subset (an unsatisfiable core) that is responsible for the failure. The identified core is then used to split the current subset into smaller ones. By combining this top-down scheme with a set-covering algorithm, we derive an overall approach that provides optimal PWA models for a given error tolerance, where optimality refers to minimizing the number of pieces of the PWA model. We demonstrate our approach on three numerical examples that include PWA approximations of a widely used nonlinear insulin–glucose regulation model and a double inverted pendulum with soft contacts.

A new control strategy for a class of piecewise deterministic processes (PDP) is presented. In this class, PDP stochastic processes consist of ordinary differential equations that are subject to random switches corresponding to a discrete Markov process. The proposed strategy aims at controlling the probability density function (PDF) of the PDP. The optimal control formulation is based on the hyperbolic Fokker–Planck system that governs the time evolution of the PDF of the PDP and on tracking objectives of terminal configuration with a target PDF. The corresponding optimization problems are formulated as a sequence of open-loop hyperbolic optimality systems following a model predictive control framework. These systems are discretized by first-order schemes that guarantee positivity and conservativeness of the numerical PDF solution. The effectiveness of the proposed computational control framework is validated considering PDP with dichotomic noise.

This paper presents a control architecture, which has the potential to monitor the task and safety issues, to provide assessment of the progress and alter the task parameters, and to incorporate patient's feedback in order to make the necessary modifications to impart effective therapy during the execution of the task in an automated manner. Experimental results are presented to demonstrate the efficacy of the proposed control architecture.

Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise in the system is taken into account.

Newell (1980; 1990) proposed that cognitive theories be developed in an effort to satisfy multiple criteria and to avoid theoretical myopia. He provided two overlapping lists of 13 criteria that the human cognitive architecture would have to satisfy in order to be functional. We have distilled these into 12 criteria: flexible behavior, real-time performance, adaptive behavior, vast knowledge base, dynamic behavior, knowledge integration, natural language, learning, development, evolution, and brain realization. There would be greater theoretical progress if we evaluated theories by a broad set of criteria such as these and attended to the weaknesses such evaluations revealed. To illustrate how theories can be evaluated we apply these criteria to both classical connectionism (McClelland & Rumelhart 1986; Rumelhart & McClelland 1986b) and the ACT-R theory (Anderson & Lebiere 1998). The strengths of classical connectionism on this test derive from its intense effort in addressing empirical phenomena in such domains as language and cognitive development. Its weaknesses derive from its failure to acknowledge a symbolic level to thought. In contrast, ACT-R includes both symbolic and subsymbolic components. The strengths of the ACT-R theory derive from its tight integration of the symbolic component with the subsymbolic component. Its weaknesses largely derive from its failure, as yet, to adequately engage in intensive analyses of issues related to certain criteria on Newell's list.

We present methods and tools from the Soft Computing (SC) domain, which is used within the diagnostics and prognostics framework to accommodate imprecision of real systems. SC is an association of computing methodologies that includes as its principal members fuzzy, neural, evolutionary, and probabilistic computing. These methodologies enable us to deal with imprecise, uncertain data and incomplete domain knowledge typically encountered in real-world applications. We outline the advantages and disadvantages of these methodologies and show how they can be combined to create synergistic hybrid SC systems. We conclude the paper with a description of successful SC case study applications to equipment diagnostics.

The notion of a bisimulation relation is of basic importance in many areas of computation theory and logic. Of late, it has come to take a particular significance in work on the formal analysis and verification of hybrid control systems, where system properties are expressible by formulas of the modal μ-calculus or weaker temporal logics. Our purpose here is to give an analysis of the concept of bisimulation, starting with the observation that the zig-zag conditions are suggestive of some form of continuity. We give a topological characterization of bisimularity for preorders, and then use the topology as a route to examining the algebraic semantics for the µ-calculus, developed in recent work of Kwiatkowska et al., and its relation to the standard set-theoretic semantics. In our setting, μ-calculus sentences evaluate as clopen sets of an Alexandroff topology, rather than as clopens of a (compact, Hausdorff) Stone topology, as arises in the Stone space representation of Boolean algebras (with operators). The paper concludes by applying the topological characterization to obtain the decidability of μ-calculus properties for a class of first-order definable hybrid dynamical systems, slightly extending and considerably simplifying the proof of a recent result of Lafferriere et al.

For a hybrid system composed of a cable with masses at both ends, we prove the existence of solutions for a class of nonlinear and nonmonotone feedback laws by means of a priori estimates. Assuming some local monotonicity, strong stabilization is obtained thanks to some Riemann's invariants technique and La Salle's principle.