This paper addresses discrete-time least-squares estimation in a behavioral framework. Firstly, we formulate the problem we attack here in a behavioral setting. Next, we provide some new results on polynomial matrices, spectral factorizations and dissipation theory. By using these new results, we then give a necessary and sufficient condition for a latent variable to yield the optimal estimation of the measured signal with observations on the theoretical differences between the discrete-and the continuous-time case. Then, we discuss issues on the implementation of the optimal estimator and we give a real-time algorithm so as to obtain the optimal estimation on-line. In order to show the validity of the results, we also give a simple numerical example.
This paper considers methods for regional robust l2 performance analysis and its state feedback control synthesis of linear time invariant discrete-time systems with saturation nonlinearities via a polytopic approach for the nonlinearities. For the analysis and synthesis, a domain of l2 performance is defined as a domain of initial states guaranteed with l2 performance and exponential stability one. The solvability conditions of the analysis and synthesis problem based on the domain can be recasted as linear matrix inequalities via level sets of quadratic Lyapunov functions, the polytopic approach and constant scaling matrices for the robustness. However, the single state feedback gain without switching cannot achieve non-conservative control performance due to evaluating an admissible set of the exogenous inputs to be large. Specifically, when the exogenous input, the state and the performance output are measurable such as a tracking control problem for servo control systems, this paper proposes a switching control of the state feedback gains designed by the derived synthesis conditions using off-line computation in order to reduce conservativeness of the results without the switching. Finally, this paper verifies effectiveness of our proposed switching control method through a simulation and an experiment.
The graphing calculator, Voyage200, is a calculator which has the Derive system as a computational engine and can do symbolic manipulation. It has a large liquid crystal display (128 × 240 pixels) as for a calculator and various responses can be drawn on it. Furthermore, it can be easy to make user-defined functions on it and extend to solve specified problems. Taking notice of the high potential and its portability, we develop the library for analysis and synthesis of linear control systems. In this paper, we introduce typical programs including our library which consists of programs more than 100 and examine the effectiveness at the stand point of control education. According to the results of several examples, our system may be available for the 4th order systems or less, as regards computational time. However, it must be enough as education of the beginners of control engineering and powerful handheld tool.
The present study considers a new slack-based strategy for project scheduling, which introduces dummies. A dummy corresponds to an unforced slack time and is used for absorption of schedule delays caused by disturbances during the schedule execution. In this paper, we propose a mathematical model for determining an optimal dummy size K* to be inserted into a baseline schedule of a given project, considering the costs for dummies as well as those for schedule delays caused by disturbances. We first describe the concept of dummy and then formulate the total expected cost of a schedule with dummies. Clarified are the conditions on which a unique finite optimal dummy size K* exists, where the total expected cost is minimized. We also discuss the characteristics and the effectiveness of the proposed model through some numerical examples.
Exact robust H2 performance analysis is considered for linear time-invariant systems whose coefficient matrices are polynomials of a single parameter. A necessary and sufficient condition for the robust H2 performance is derived as a set of parameterized LMIs whose variable matrix is a polynomial of the parameter, where a bound of its degree is given explicitly. Then, the parameterized LMIs are transformed exactly to parameter-independent and finite-dimensional LMIs.