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In this paper, we propose a design method of average state Kalman filters for networked linear systems with stochastic noises. The average state Kalman filter is a low-dimensional estimator capturing the average behavior of systems from a macroscopic point of view. In general, it is nontrivial to find a set of states that captures the average behavior of systems. To overcome this difficulty, using the notion of clustering, we devise a systematic design procedure of average state Kalman filters while determining states that capture the average behavior of systems. Furthermore, deriving a tractable representation of the estimation error system, we derive an estimation error bound for the proposed method in a theoretical way. The efficiency of the proposed method is shown by a power system example in smart grid applications.

This paper proposes a new system model called a positive quadratic system for molecular interaction in a cell, including a signal transduction pathway and a gene regulatory pathway. Although the whole network of these pathways is far more complex than simple chemical reactions, one of the features of the proposed model is that it can capture the quadratic property of molecular interaction as well as the positivity properties of the state variables with a rather simple form. Based on this model, we derive a sufficient condition of the stability in the sense of Lyapunov, and present a method for estimating a positive invariant set depending on the initial state. We show that the proposed method is effective by numerical simulations of two fundamental biological models.

This paper deals with model predictive control of continuous-time piecewise affine (CTPWA) systems. First, the finitehorizon optimal control problem of CTPWA systems is reduced, with certain suboptimality, to the optimization problem of mode sequences and intermediate state sequences. Next, an implementation method based on a precomputation technique is proposed. In the offline phase, this method computes, for every mode sequence, the set of feasible initial states and a lower bound of the cost function associated with it. Then at each sampling time in the online phase, the controller determines the optimal mode sequence and the optimal intermediate state sequence over a prediction horizon, taking advantage of the precomputed information. By effectively distributing the computation over the offline phase and the online phase, real-time control is achieved, striking a good balance between the amount of precomputed data and the online computation time. The effectiveness of the proposed method has been evaluated with a simple exapmle of CTPWA systems by numerical simulations.

This paper proposes a novel efficient algorithm for model predictive control (MPC) of input-constrained linear systems. Based on the fact that the problem of MPC is reduced into the problem of calculating the solution trajectory of the discrete-time linear complementarity (D-LC) systems, the proposed algorithm fully exploits the information on the solution of the problem at the previous time step, as like the difference technique used in the calculation of solution trajectories of a dynamical system. It is shown that the proposed algorithm is much more efficient than the other conventional algorithms at a large prediction horizon.

This paper proposes a new approach to solve the controllability (reachability) problem of the sampled-data/discrete-time piecewise affine systems. First, an algebraic characterization for the system to be controllable/reachable is derived. Next, based on this characterization, an approach to determine if the system is controllable/reachable in a probabilistic sense is proposed based on a randomized algorithm. Finally, it is shown by numerical examples that the proposed approach is useful.

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.