Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in Japa

Nonlinear and adaptive control

The primary thrust of the research was to conduct fundamental research in the theories and methodologies for designing complex high-performance multivariable feedback control systems; and to conduct feasibiltiy studies in application areas of interest to NASA sponsors that point out advantages and shortcomings of available control system design methodologies

Shaping Pulses to Control Bistable Biological Systems

In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulse-based control comes from applications in synthetic biology, where it is generally difficult to implement real-time feedback control systems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set of all pulses that switch the system reduces to the computation of one non-increasing curve. We provide an efficient algorithm to compute this curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results to models with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitations of the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotone biochemical system using a combination of temporal pulses and event-based control. Our results provide an insight into the dynamics of bistable systems under external inputs and open up numerous directions for future investigation.Comment: 14 pages, contains material from the paper in Proc Amer Control Conf 2015, (pp. 3138-3143) and "Shaping pulses to control bistable systems analysis, computation and counterexamples", which is due to appear in Automatic

Input-Output-to-State Stability

This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of ``norm-estimators'', and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.Comment: Many related papers can be found in: http://www.math.rutgers.edu/~sonta

Design of Control Systems with Multiple Backlash Nonlinearities Subject to Inputs Restricted in Magnitude and Slope

This paper develops a computational method for designing a control system that is an interconnection of transfer functions and multiple decoupled backlash nonlinearities where each backlash is modelled as an uncertain band containing multi-valued functions. The design objective is to ensure that the system outputs and the nonlinearity inputs always stay within their prescribed bounds in the presence of all inputs whose magnitude and whose slope are bounded by respective numbers. By using a known technique, each backlash is decomposed as a linear gain and a bounded disturbance. Essentially, the original design problem is replaced by a surrogate design problem that is related to a linear system and thereby can readily be solved by tools available in previous work. Moreover, as a result of using the convolution algebra A, the method developed here is applicable to rational and nonrational transfer functions. To illustrate the usefulness of the method, linear decentralized controllers are designed for a binary distillation column where valve stiction characteristics are taken into account