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In this paper, we revisit the full lattice representation of continuous piecewise affine (PWA) functions and give a formal proof of its representation ability. Based on this, we derive the irredundant lattice PWA representations through removal of redundant terms and literals. Necessary and sufficient conditions for irredundancy are proposed. Besides, we explain how to remove terms and literals in order to ensure irredundancy. An algorithm is given to obtain an irredundant lattice PWA representation. In the worked examples, the irredundant lattice PWA representations are used to express the optimal solution of explicit model predictive control problems, and the results turn out to be much more compact than those given by a state-of-the-art algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a method to estimate the domain of attraction of a class of discrete-time Lur’e systems is presented. A new notion of invariance, denoted -invariance, is introduced. An algorithm to determinate the largest -invariant set for this class of systems is proposed. Moreover, it is proven that the -invariant sets provided by this algorithm are polyhedral convex sets and constitute an estimation of the domain of attraction of the non-linear system. It is shown that any contractive set for the Lur’e system is contained in the -invariant set obtained applying the results of this paper. Two illustrative examples are given. [Copyright &y& Elsevier]

This paper focuses on sensor scheduling for state estimation, which consists of a network of noisy sensors and a discrete-time linear system with process noise. As an energy constraint, only a subset of sensors can take a measurement at each time step. These measurements are fused into a common state estimate using a Kalman filter and the goal is to schedule the sensors to minimize the estimation error at a terminal time. A simple approach is to greedily choose sensors at each time step to minimize the estimation error at the next time step. Recent work has shown that this greedy algorithm outperforms other well known approaches. Results have been established to show that the estimation error is a submodular function of the sensor schedule; submodular functions have a diminishing returns property that ensures the greedy algorithm yields near optimal performance. As a negative result, we show that most commonly-used estimation error metrics are not, in general, submodular functions. This disproves an established result. We then provide sufficient conditions on the system for which the estimation error is a submodular function of the sensor schedule, and thus the greedy algorithm yields performance guarantees. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problems of parameter estimation are addressed for systems with scarce measurements. A gradient-based algorithm is derived to estimate the parameters of the input–output representation with scarce measurements, and the convergence properties of the parameter estimation and unavailable output estimation are established using the Kronecker lemma and the deterministic version of the martingale convergence theorem. Finally, an example is provided to demonstrate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we study the identification of parametric Hammerstein systems with FIR linear parts. By a proper normalization and a clever characterization, it is shown that the average squared error cost function for identification can be expressed in terms of the inner product between the true but unknown parameter vector and its estimate. Further, the cost function is concave in the inner product and linear in the inner product square. Therefore, the identification of parametric Hammerstein systems with FIR linear parts is a globally convergent problem and has one and only one (local and global) minimum. This implies that the identification of such systems is a linear problem in terms of the inner product square and any local search based identification algorithm converges globally. [Copyright &y& Elsevier]

Abstract: The paper presents a unified perspective on geometric and algebraic criteria for reachability and controllability of controlled switched linear discrete-time systems. Direct connections between geometric and algebraic criteria are established as well as that between the subspace based controllability/reachability algorithm and Kalman-type algebraic rank criteria. Also the existing geometric criteria is simplified and new algebraic conditions on controllability and reachability are given. [Copyright &y& Elsevier]

Abstract: This paper deals with the stabilizability of interconnected systems via linear time-invariant (LTI) decentralized controllers. Given a controllable and observable system with some distinct decentralized fixed modes (DFMs), it is desired to find a suitable control structure (in terms of information flow) for it. Since a decentralized controller consists of a number of non-interacting local controllers, the objective here is to establish certain interactions between the local controllers in order to eliminate the undesirable DFMs. This objective is achieved by translating the knowledge of the system into some bipartite graphs. Then, the notions of minimal sets and maximal subgraphs are introduced, which lead to a simple combinatorial algorithm for solving the underlying problem. The efficacy of the results obtained is demonstrated by an illustrative example. [Copyright &y& Elsevier]

Abstract: A generalized relay identification method is proposed in this paper for time delay and non-minimum phase processes. A distinct merit of the proposed method is that the process gain can be uniformly derived from a single run of the relay test, independent of the relay type being unbiased or biased. An analytical relay response expression is derived for assessing the process response under an unbiased or biased relay test. A frequency response algorithm is also derived for estimating the multiple frequency response points of the process. By categorizing cases of the model parameters to be identified, the corresponding identification algorithms are developed using fitting conditions established for the process response at the oscillation frequency. Based on the improved estimation of multiple frequency response points, a recursive least-squares identification algorithm is then proposed for obtaining further enhanced fitting accuracy over a user specified frequency range, e.g., the low frequency range often concerned in practical controller tuning. Illustrative examples from the recent literature are given to demonstrate the effectiveness and merits of the proposed algorithms. [Copyright &y& Elsevier]

Abstract: A consensus problem consists of finding a distributed control strategy that brings the state or output of a group of agents to a common value, a consensus point. In this paper, we propose a negotiation algorithm that computes an optimal consensus point for agents modeled as linear control systems subject to convex input constraints and linear state constraints. By primal decomposition and incremental subgradient methods, it is shown that the algorithm can be implemented such that each agent exchanges only a small amount of information per iteration with its neighbors. [Copyright &y& Elsevier]

Abstract: Holonic manufacturing systems (HMS) is based on the notion of holon, an autonomous, cooperative and intelligent entity to provide a econfigurable, flexible and decentralized manufacturing environment to respond to changing needs and opportunities. A set of holons that cooperate to achieve a goal forms a holarchy. How to design a mechanism to form a holarchy to achieve a goal while minimizing the overall cost is a challenge. The objectives of this paper are to propose models and develop collaborative algorithms to guide the holons to form a holarchy to coherently move toward the desired goal state ultimately. We adopt contract net protocol (CNP) to model mutual selection of holons in forming a holarchy. We formulate a holarchy optimization problem to minimize the cost subject to the feasibility constraints. To analyze the feasibility of a holarchy, a Petri net (PN) model is proposed. As classical PN models do not take into account the cost involved in firing transitions, we augment the PN model with cost functions in the problem formulation. Due to the distributed architecture of HMS, the internal structure of each potential holarchy that acts as bidder in CNP is not available to the manager. A key issue is to determine the feasibility of a holarchy without constructing the whole PN model of the given hierarchy. We study the feasible conditions for a holarchy and propose a collaborative algorithm to analyze the feasibility and award contracts to holons without constructing the whole model of a holarchy. [Copyright &y& Elsevier]