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This paper proposes a box expanding method to reduce the economic dispatch (ED) cost in the box-based robust unit commitment model (BUC). As a non-anticipative robust unit commitment model for a power system under demand uncertainty, BUC co-optimizes the commitment schedule and the feasible set of the ED problem to minimize the total operating cost for the worst-case realization in a set of possible demand scenarios; the feasible set of the ED problem is modeled as a box to enable the non-anticipative real-time dispatch. Meanwhile, as BUC considers the worst-case total operating cost, the actual total operating cost may be unnecessarily high. In this paper, the box feasible set of the ED problem in BUC is expanded to a larger one via multi-objective optimization with a no-preference method. The expanded box forms a new feasible set of the ED problem, which increases the chance of reducing the actual ED cost and thus the actual total operating cost. Simulation results using 5-, 14-, and 30-bus test systems demonstrate the effectiveness and generality of the proposed method.

For safe and efficient driving of a vehicle on urban roads, it is essential to analyze the trends of the vehicles ahead to take early measures in changing traffic situations. Existing efficient driving systems based on optimal car following compute the vehicle control input by solving an optimization problem over a prediction horizon, and at the expense of large computation cost, they provide significant improvement in traffic flows and fuel consumption. This paper proposes a look-ahead car following scheme, which can take anticipatory driving decisions with negligible computation cost, for efficient driving of a vehicle. Specifically, at first, the distinctive features of an optimal car following scheme over traditional car following of a human driver are investigated. Then, based on the features observed, a look-ahead car following scheme is formulated that can partly reflect the desired driving characteristics of the optimal car following scheme. The proposed scheme extends a traditional car following model by incorporating the predicted state of the preceding vehicle in a restricted look-ahead horizon. Finally, the proposed look-ahead car following scheme is evaluated in typical urban traffic scenarios, and the observed driving characteristics and performances are compared.

In this paper, we develop a distributed design method for power system stabilizers (PSSs) that improve damping performance for deflections caused by contingencies in a power grid in which large-scale PV penetration is introduced. We suppose that there are multiple independent system operators in a grid and each system operator designs a PSS based on the corresponding subsystem model information alone. The controller design method for PSSs under the restriction on available model information is called distributed design. Although practical distributed design methods are typically based on single-machine infinite-bus system, the problem here is that the designed controller possibly destabilizes the grid. In this paper, we propose a novel distributed design method for power grids based on retrofit control theory. The designed PSS can theoretically guarantee the stability of power grids and also improves damping performance. Through a numerical example for the IEEJ EAST 30-machine power system, the effectiveness of our proposed method is verified compared with the conventional method.

This paper focuses on the day-ahead scheduling problem of generating power for thermal power plants and charging/discharging battery energy storage systems based on interval predictions of photovoltaic power. Our previous approach to this problem used the Jacobian of a solution with respect to the variation in demand. However, this study was limited in the sense that the output capacity constraints of thermal power plants were not taken into account. To overcome this problem, we introduce a virtual thermal plant and apply several properties of an M -matrix. To provide guidelines for the amount of power that should be generated, we determine the exact regulating capacity for each thermal power plant and a storage battery so as to maintain the supply–demand balance. The efficiency of the proposed method is verified numerically. We show that a brute-force Monte Carlo method cannot estimate the exact regulating capacity of the thermal power plants when the batteries effectively balance the supply and demand. Moreover, it is found that, unless their deterioration cost decreases significantly, storage batteries cannot be effectively utilized.

In this paper, we formulate an optimal bidding problem in a multiperiod electricity market with the consideration of the uncertain PV output. Based on the proposed strategy, the aggregator of interest operates his dispatchable assets to pursue the largest profit by submitting one optimal prosumption curve to the day-ahead market. To deal with a non-convexity issue stemming from the robust optimization problem, we reformulate the problem as its Lagrange dual counterpart. Then, we describe the uncertain range of the PV output by one polyhedral set, with which a new decision variable is introduced. We implement a constraints-generation method to solve the newly formulated problem by splitting it into another two subproblems. Based on one iterative scheme, the two subproblems are solved in sequence, and the solution of the robust optimization problem is obtained when the optimal results of the two subproblems are equal. In the numerical simulation, the profits under different PV lower bounds are presented.

How to construct a reliable deoxyribonucleic acid (DNA) circuit is one of the most important issues in the field of molecular programming and computing. Such a circuit frequently suffers from various kinds of unintended binding reactions on account of a lower specificity of the molecular interaction emerging from base complementarity between DNA strands, which results in low reliability of the molecular circuit. In this study, we propose a method to quantitatively evaluate the robustness of a DNA circuit created by DNA strand displacement reactions. The highlight of our method is representing the circuit system contaminated by unintended reactions by a standard form of a disturbed nonlinear system and evaluating the robustness with the L2 gain by solving the Hamilton–Jacobi inequality.

In this paper, we formulate a problem of power profile market clearing and develop a distributed market clearing scheme with explicit consideration of high battery penetration. The power profile market is a multiperiod electricity market in which each aggregator aims at making the highest profit by transacting a power profile, i.e., a time sequence of energy amounts at several time slots, that is generated by dispatchable power generation as well as the charge and discharge of batteries. It is theoretically shown that the clearing price profile during the time period of interest tends to level off in the high penetration of batteries. This finding enables to develop a distributed market clearing scheme that is implemented as a bidding strategy for the total energy amount during the period followed by a distributed iterative algorithm for profile imbalance minimization. Numerical simulations demonstrate the price leveling-off led by high battery penetration and the efficiency of the proposed distributed scheme.

This paper studies a day-ahead scheduling problem on power generation of thermal power plants and charge/discharge of battery energy storage systems, where the confidence intervals of the prediction of photovoltaic (PV) and demand power are available. This problem is reduced to an interval optimization problem, where parameters having any values in certain intervals are included. We have developed a method for efficiently solving this kind of problems using tools from the interval analysis. However, the class of the problem that we have studied there is limited in the sense that the output capacity constraints of thermal power plants are not taken into account. This paper proposes a new method for efficiently solving a more practical scheduling problem with the capacity constraints of thermal power plants added. To use our method, we need to analyze a matrix corresponding to a Jacobian of a solution to an optimization with respect to parameters on demand deviation, which is too complex to analyze in general. The key to overcome this difficulty is that we introduce a virtual thermal power plant whose output capacity constraint is not imposed. By using this idea, we can transform the above matrix into an appropriate matrix that is analyzed as easily as possible. The efficiency of the proposed method is shown by numerical simulations on the power system in the Tokyo area.

In this paper, we propose a design method of distributed temperature regulators for an air conditioning system, which is modeled as a network system composed of second-order subsystems representing the dynamics of air conditioners and thermal diffusion among areas. In the proposed method, to make a distributed regulator design problem tractable, we consider confining the class of distributed controllers to that consisting of second-order subcontrollers, whose network structure is made identical to that of the controlled system. On the basis of this specialization, we derive a necessary and sufficient condition of stabilizing controller parameters. Furthermore, we show that the problem of distributed regulator design can be reduced to a problem of robust state feedback gain design, formulated as guaranteeing a control specification in terms of the H2- and H∞-norm. The efficiency of our distributed regulator design method is shown through a couple of numerical simulations.

International audience; This paper proposes a clustered model reduction method for semistable positive linear systems evolving over directed networks. In this method, we construct a set of clusters, i.e., disjoint sets of state variables, based on a notion of cluster reducibility, defined as the uncontrollability of local states. By aggregating the reducible clusters with aggregation coefficients associated with the Frobenius eigenvector, we obtain an approximate model that preserves not only a network structure among clusters, but also several fundamental properties, such as semistability, positivity, and steady state characteristics. Furthermore, it is found that the cluster reducibility can be characterized for semistable systems based on a projected controllability Gramian that leads to an a priori H2-error bound of the state discrepancy caused by aggregation. The efficiency of the proposed method is demonstrated through an illustrative example of enzyme-catalyzed reaction systems described by a chemical master equation. This captures the time evolution of chemical reaction systems in terms of a set of ordinary differential equations.

Our previous study proposed a positive quadratic system representation for molecular interaction in a cell, including a signal transduction pathway and a gene regulatory network, and also presented a method for estimating a positive invariant set depending on the initial state. As an extension towards wider applications of this approach, this paper proposes a system representation called here a singularly perturbed positive quadratic system, and shows that every positive rational system, which is used as a mathematical model expressing biological behavior, can be approximately represented by a quasi-steady state system of a singularly perturbed positive quadratic system. In addition, we prove that the singularly perturbed positive quadratic system preserves stability at an equilibrium point of the positive rational system.

In this report, for a reheating furnace, which is employed in one of the processes for producing steel sheets from slabs, we propose a modelling method that simultaneously optimizes both the permutation scheduling of slabs and the heat controlling of the furnace. The proposed modelling scheme is based on a hybrid model composed of a nonlinear advection equation that expresses the behavior of the slab temperature and a discrete model for feeding slabs. The model predictive control problem of this model, which will be reduced to a mixed integer programming problem, is formulated by discretizing the advection equation in time and space by means of the method of characteristics and spatially piecewise-linearizing the nonlinear term. It is shown by numerical simulations that the proposed model predictive control method is very effective from the viewpoint of the control performance and the computational burden.

We analyze the robustness of a system-level genetic circuit which is constructed by a bottom-up strategy. The latest trend in synthetic biology is to create large-scale and complex genetic circuits realizing desired programmable functions. An approach for the creation is bottom-up construction, that is, well-characterized small-scale circuits are coupled into large-scale system-level circuits involving desired programmable functions that can be predicted from the modules. However, in general, an intrinsic property in a circuit may be broken by internally connecting external circuits. We analyze a successful circuit created by a bottom-up construction strategy to identify the reason behind a successful synthesis. Utilizing the robustness analysis method based on the structured singular value, we can guarantee the validity of the bottom-up construction.

We investigate the convergence rates of diffusion in bidirectional Erdos–Renyi networks. We analytically and numerically demonstrate that the asymptotic distribution is far from a bell shape. Further, we numerically verify that the dynamical networks generated by the Barabasi–Albert model, which is a standard scale-free network model, exhibiting faster convergence of average consensus.

As is well known, the computational complexity in the mixed integer programming (MIP) problem is one of the main issues in model predictive control (MPC) of hybrid systems such as mixed logical dynamical systems. Thus several efficient MIP solvers such as multi-parametric MIP solvers have been extensively developed to cope with this problem. On the other hand, as an alternative approach to this issue, this paper addresses how a deterministic finite automaton, which is a part of a hybrid system, should be expressed to efficiently solve the MIP problem to which the MPC problem is reduced. More specifically, a modeling method to represent a deterministic finite automaton in the form of a linear state equation with a smaller set of binary input variables and binary linear inequalities is proposed. After a motivating example is described, a derivation procedure of a linear state equation with linear inequalities representing a deterministic finite automaton is proposed as three steps; modeling via an implicit system, coordinate transformation to a linear state equation, and state feedback binarization. Various significant properties on the proposed modeling are also presented throughout the proofs on the derivation procedure.

It is well known that the state estimation of nonlinear systems with noise is efficiently performed by unscented Kalman filters. However, they assume that the dynamics of the system is known in advance. Hence, this paper focuses on the state estimation problem of unknown chaotic dynamical systems with the recurrent property, and proposes a model-free unscented Kalman filter method for such systems, where the modified method of analogues developed in the field of nonlinear time series analysis is used. Effectiveness of this method is shown by numerical simulations.

This paper discusses oscillation analysis of (a large number of) linearly coupled piecewise affine (PWA) systems, motivated by various kinds of reaction-diffusion systems including cell-signaling dynamics and neural dynamics. We derive a sufficient condition under which the system shows an oscillatory behavior called Y-oscillation. It is known that the analysis of PWA systems is difficult due to their switching nature. An important feature of the result obtained is that, under the assumption that every subsystem has a specific property in common, the criteria can be rewritten in terms of coupling topology in an easily checkable way, so it is applicable to large scale systems. The results obtained are applied to theoretical investigation of the cardiac action potential generation/propagation represented by spatio-temporal FitzHugh-Nagumo equations.

An algorithm for evaluating the cost performance of discontinuous autonomous discrete-time piecewise affine systems is presented. The algorithm performs reverse reachability analysis and constructs a piecewise quadratic trajectory cost function over the entire region of attraction of the origin while explicitly taking into account the exact spatial evolution of the trajectories and the exact switching structure of the system as a whole. Available explicitly, this cost function can be integrated in order to evaluate the cost performance of the entire system. The reverse reachability algorithm is applied to the problem of constructing Lyapunov functions. The resulting Lyapunov functions are less conservative than other forms of Lyapunov function commonly used for stability analysis of autonomous discrete-time piecewise affine systems.

Time-invariant input-move-blocking regimes are used in many practical online model predictive control systems in order to reduce the computational complexity of the associated finite-horizon optimal control problem, and have been shown to be beneficial for offline model predictive control methods also. However, until now there exists no method to ensure strong feasibility. In this paper a least-restrictive method to enforce strong feasibility in time-invariant input-move-blocking model predictive control problems is proposed, where the state of the first prediction step is constrained to a novel type of controlled invariant set, called here a controlled invariant feasible set. An algorithm to determine maximal controlled invariant feasible sets is proposed. This algorithm is shown to be semi-decidable for the case of linear, time-invariant plants with time-invariant, polytopic state and control input constraint sets.

This paper discusses the optimal control problem of the continuous-time piecewise affine (PWA) systems with sampled-data switching, where the switching action is executed based upon a condition on the state at each sampling time. First, an algebraic characterization for the problem to be feasible is derived. Next, an optimal continuous-time controller is derived for a general class of PWA systems with sampled-data switching, for which the optimal control problem is feasible but whose subsystems in some modes may be uncontrollable in the usual sense. Finally, as an application of the proposed approach, the high-speed and energy-saving control problem of the CPU processing is formulated, and the validity of the proposed methods is shown by numerical simulations.

This paper discusses a two-sided error probabilistic approach to the controllability analysis of the discrete-time PWA systems. First, the two onesided error probabilistic approaches, which have been recently proposed by the authors, are surveyed. Next, as a natural extension of these two algorithms, a polynomial-time two-sided error randomized algorithm for approximately verifying the controllability is derived. Finally, the features of the three algorithms are compared, and then it is shown by some examples that the proposed approach is computationally useful.

This paper discusses from the algebraic points of view the relationship among the four properties of discrete-time piecewise linear systems; observability, determinability, mode estimability, and mode-sequence estimability. First, necessary and sufficient conditions for the system to be determinable, and to be mode- sequence estimable are derived. Next, the observability property is characterized in terms of those conditions. Finally, the relationship between the observability property of the original system and the well-posedness property of the time- reversed system is discussed.

This paper discusses an on-line approach to Model Predictive Control (MPC) of input constrained linear systems. First, it is shown that an example of MPC with one-side input constraints is reduced into the Linear Complementarity (LC) Problem with M -matrix, which can be more efficiently solved by the existing special algorithm than the other general algorithms such as the Lemke method. However, in the case of both-side input constraints, which is more practical from the control engineering points of view, it cannot be reduced into the LC problem with M -matrix. Thus, next, a new algorithm for the case of both-side input constraints is proposed in this paper.

This paper discusses the optimal continuous-time control problem of a class of piecewise affine (PWA) systems, where the switching action of the discrete state is determined at each sampling time according to a condition on the continuous state. Such a system is called here the sampled-data PWA (SD-PWA) system. First, important remarks on the control design of this system via the continuous-(or discrete-)time PWA model are pointed out, which motivate us to use the SD-PWA model. Next, based on the good properties of the proposed model, an optimal continuous-time controller of the SD-PWA systems is proposed.

This paper discusses the controllability problem for a class of continuoustime piecewise affine (PWA) systems with the sampled-data autonomous switching, which we call here the sampled-data PWA systems. First, the four concepts of controllability are introduced based on the aspects of the continuous/discrete state and of the continuous/discrete time, and some inclusion relations among them are discussed. Next, easily checkable, (necessary and) sufficient conditions for the system to be controllable are derived

The well-posedness (existence and uniqueness of solutions) problem and the stabilization problem of switch-driven piecewise affine (PWA) systems with 2 binary switches are addressed. First, under some assumptions, a necessary and sufficient condition for the system to be well-posed is derived. Next, based on this result, an approach to find a dynamic state feedback controller for which the closed loop system is well-posed as well as globally asymptotically stable is proposed.

This paper develops a new approach to the parametrization of all asymptotically stabilizing controllers of nonlinear systems including time-varying ones, both for state feedback and output feedback. Assumptions of stabilizability and a kind of detectability are required. The approach is very direct and simple, and is not based on the so-called factorization and on the H∞ framework of nonlinear systems which are used in previous papers. A key of the derivation of the parametrization in this paper is to find an explicit state space representation of free functions, such that the parametrized controller expresses all asymptotically stabilizing controllers of nonlinear systems.

This paper gives a characterization of three gain conditions, i.e., L 2∞ gain, L 2∞ gain subject to an L 2 gain constraint, and the Hankel gain, of nonlinear systems via the Hamilton-Jacobi inequalities. It is shown that the obtained results for the L 2∞ gain and the Hankel gain are analog to that derived for the L 2 gain so far.

A Hamilton-Jacobi strict inequality approach is developed for the strict H8 control problem of nonlinear systems. First, a characterization of the strict bounded real condition of nonlinear systems is given by the Hamilton-Jacobi strict inequality. Next, based on the above result, some necessary and/or sufficient conditions are given for the solvability of the strict H8 control problem via state and output feedback in the case of asymptotic stability.

This paper is concerned with robust stabilization of nonlinear systems with unstructured uncertainty via state feedback. First, a robust stability condition is given for a closed loop system which is composed of a nonlinear nominal system and an unstructured uncertainty. Second, based on the obtained robust stability condition, a sufficient condition for robust stabilization by state feedback is given in terms of the solvability of some H ∞ state feedback control.

Taking account of the plant nonlinearity, we propose a controller design method which consists of H∞ control and exact linearization via nonlinear state feedback. The latter one is designed to yield the linear system which exactly equals to the linearization of the plant around an equilibrium point. We illustrate the validity of our method by experiments.