A bound on closed-loop performance based on finite-frequency response samples

A new, computationally tractable, bound is derived for the level of closed-loop performance achieved by a given finite-dimensional feedback compensator with a plant for which a finite number of frequency response samples are computable. The bound involves quantities reflecting the performance of the controller with a finite-dimensional, nominal model of the plant, quantities that can be determined from the finite number of frequency response samples of the true plant, and quantities related to the complexity (in the sense of Vinnicombe) of all systems involved. This bound can be used to ‘validate’ closed-loop performance in the case that the true plant frequency response samples are of a plant which is not completely known or, to measure the performance of a finite-dimensional controller with a computationally intractable (e.g. infinite-dimensional) model of the true plant.     

On validating closed-loop behaviour from noisy frequency-response measurements

It is shown how noisy closed-loop frequency-response measurements can be used to obtain pointwise in frequency bounds on the possible difference between the actual closed-loop system and the closed-loop comprising a nominal model of the plant and the stabilising controller. To this end, Vinnicombe's gap metric framework for robustness analysis plays a central role. Indeed, an optimisation problem and corresponding algorithm are proposed for estimating the chordal distance between the frequency responses of the nominal plant model and a plant that is consistent with the closed-loop data and a priori information, when projected onto the Riemann sphere.     

Robust control design for best mean performance over an uncertain-parameters box

This paper deals with robust, polytopic, probabilistic H_∞ analysis and state-feedback synthesis of linear systems and focuses on the performance distribution over the uncertainty region (rather than on the performance bound). The proposed approach allows different disturbance attenuation levels (DALs) at the vertices of the uncertainty polytope. It is shown that the mean disturbance attenuation level (DAL) over an uncertain parameters-box is the average of the DALs at the vertices, if each parameter has an independent, symmetrical, centered probability density function. In such a (most common) case, the mean DAL over the uncertain parameters-box can be optimized by minimizing the sum of the DALs at the vertices. The standard deviation of the DAL over the uncertain parameters-box is also addressed, and a method to minimize this standard deviation is shown. A new robust H_∞ state-feedback synthesis theorem is given; it is based on a recent, most efficient analysis method and applies the proposed multiple-vertex-DALs approach. A state-feedback design example utilizing the latter theorem shows that a control design which minimizes the sum of the vertex-DALs leads to a better actual closed-loop performance than a similar design which minimizes only the bound of the DAL over the uncertainty polytope. The comparison is based on the statistics of a population of closed-loop ‘point-wise’ H_∞-norms created by a Monte-Carlo mechanism.     

An H-minimax approach to the design of robust control systems, part II: All solutions, all-pass form solutions and the ‘best’ solution

We characterize all solutions to a robustness optimization problem as the solutions of a two-parameter interpolation problem. From this characterization it is easy to show that an all-pass form solution always exists as long as a solution exists. We also study the possibility of using non-all-pass form solutions and by introducing other optimization objectives (motivated by improvements in disturbance rejection and robust stability) we search for the 'best' solution.     

Open Bisimulation, Revisited

In the context of the π-calculus, open bisimulation is prominent and popular due to its congruence properties and its easy implementability. Motivated by the attempt to generalise it to the spi-calculus, we offer a new, more refined definition and show in how far it coincides with the original one.     

Efficient Stochastic Simulation of Biological Systems with Multiple Variable Volumes

The application of concurrent calculi to the formalisation of biological systems constitutes a promising approach to the analysis in silico of biological phenomena. The Gillespie algorithm is one of the main models exploited for their stochastic simulation. While the original algorithm considers only one fixed-volume compartment, the simulation of biological systems often requires multi-compartment semantics. In this paper we present an enhanced formulation of an extended version of the algorithm which handles multiple compartments with varying volumes. The presented algorithm is used as basis for the implementation of an extension of the stochastic π-Calculus, called Sπ@, which allows an intuitive and concise formalisation of such systems. The algorithm is also efficient in presence of a high number of compartments and reactions, therefore Sπ@ represents the starting point for the development of an effective tool for the simulation of biological systems with dynamical structure even in presence of computationally expensive phenomena like diffusion.     

An H-minimax approach to the design of robust control systems

A realistic feedback design problem is posed based on the minimization of a weighted combination of the sensitivity and complementary sensitivity matrices. A solution is obtained which makes use of the recently proposed methods for minimizing the sensitivity function alone.     

Biological Transactions for Quantitative Models

In this work an extension of stochastic π-calculus with biological transactions is presented. This permits to model multi-reactant multi-product reactions as atomic actions when quantitative information are given. First, the syntax and the semantics are defined, then some transaction properties are discussed. Finally, some examples are described.     

A Process Model of Rho GTP-binding Proteins in the Context of Phagocytosis

At the early stages of the phagocytic signalling, Rho GTP-binding proteins play a key role. With the stimulus from the cell membrane and with the help from the regulators (GEF, GAP, Effector, GDI), these proteins serve as switches that interact with their environment in a complex manner. We present a generic process model for the Rho GTP-binding proteins, and compare it with a previous model that uses ordinary differential equations. We then extend the basic model to include the behaviour of the GDIs. We discuss the challenges this extension brings and directions of further research.     

Decentralized state-feedback stabilization and robust control of uncertain large-scale systems with integrally constrained interconnections

This paper is concerned with a problem of stabilization and robust control design for interconnected uncertain systems. A new class of uncertain large-scale systems is considered in which interconnections between subsystems as well as uncertainties in each subsystem are described by integral quadratic constraints. The problem is to design a set of local (decentralized) controllers which stabilize the overall system and guarantee robust disturbance attenuation in the presence of the uncertainty in interconnections between subsystems as well as in each subsystem. The paper presents necessary and sufficient conditions for the existence of such a controller. The proposed design is based on recent absolute stabilization and minimax optimal control results and employs solutions of a set of game-type Riccati algebraic equations arising in H_∞ control.     

A novel adaptive lattice filtering algorithm for alpha-stable processes

This paper generalizes Burg's formula to be suitable for alpha-stable distribution and proposes a novel adaptive lattice algorithm for adaptive parameter estimation of alpha-stable AR processes. The performance is compared to that of other algorithms with lattice structure for alpha-stable AR processes for different α parameter. Simulations studies indicate that the proposed algorithm shows superior convergence speed over existing well-known lattice algorithms in parameter estimation of alpha-stable processes.     

A note on the structure of two subsets of the parameter space in adaptive control problems

We study the geometric structure of two subsets of the parameter space that are of interest in the context of adaptive LQ-control. The first set can be considered as the set of possible limit points of an adaptive control algorithm, whereas the second can be seen as the set of desirable limit points. Our main result is that these sets are C^ω-manifolds.     

Robust/H∞ filtering for nonlinear systems

A robust (or H_∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed.     

Type Theory and Language Constructs for Objects with States

In current class-based Object-Oriented Programming Languages (OOPLs), object types include only static features. How to add object dynamic behaviors modeled by Harel's statecharts into object types is a challenging task. We propose adding states and state transitions, which are largely unstated in object type theory, into object type definitions and typing rules. We argue that dynamic behaviors of objects should be part of object type definitions. We propose our type theory, the τ-calculus, which refines Abadi and Cardelli's ζ-calculus, in modeling objects with their dynamic behaviors. In our proposed type theory, we also explain that a subtyping relation between object types should imply the inclusion of their dynamic behaviors. By adding states and state transitions into object types, we propose modifying programming language constructs for state tracking.     

Robust control for nonlinear systems with structured 2-gain bounded uncertainty

This paper focuses on the problem of robust control design for uncertain nonlinear systems with ₂-gain bounded dynamic uncertainty and periodically time-varying memoryless uncertainty. The robust performance problem is solved via nonlinear ^∞ control with scaling factors. It is shown that the scaling factors can be functions of state variables in contrast with linear robust control.     

Robust H∞ observer design of linear time-delay systems with parametric uncertainty

This paper deals with the problem of H_∞ observer design for a class of uncertain linear systems with delayed state and parameter uncertainties. This problem aims at designing the linear state observers such that, for all admissible parameter uncertainties, the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified H_∞ norm upper bound constraint, independently of the time delay. The time delay is assumed to be unknown, and the parameter uncertainties are allowed to be norm-bounded and appear in all the matrices of the state-space model. An effective matrix inequality methodology is developed to solve the proposed problem. We derive the conditions for the existence of the desired robust H_∞ observers, and then characterize the analytical expression of these observers in terms of some free parameters. A numerical example demonstrates the validity and applicability of the present approach.     

Robust finite horizon minimax filtering for discrete-time stochastic uncertain systems

We study a finite-horizon robust minimax filtering problem for time-varying discrete-time stochastic uncertain systems. The uncertainty in the system is characterized by a set of probability measures under which the stochastic noises, driving the system, are defined. The optimal minimax filter has been found by applying techniques of risk-sensitive LQG control. The structure and properties of resulting filter are analyzed and compared to H_∞ and Kalman filters.     

Exact computation of infimum for a class of continuous-time H∞ optimal control problem with a nonzero direct feedthrough term from the disturbance input to the controlled output

A noniterative method for the computation of infimum for a class of continuous-time H_∞ optimal control problem is considered in this paper. The problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems. The method is applicable to systems where (i) the transfer function from the disturbance input to the measurement output is free of imaginary axis invariant zeros and left invertible, and (ii) the transfer function from the control input to the controlled output of the given system is free of imaginary axis invariant zeros and right invertible. The result presented in this paper is a continuation of the previous work of the author and his co-workers (Chen et al., 1992), in which the direct feedthrough term from the disturbance input to the measurement output of the given system are required to be zero.     

Control design in the time and frequency domain using nonsmooth techniques

Significant progress in control design has been achieved by the use of nonsmooth and semi-infinite mathematical programming techniques. In contrast with LMI or BMI approaches, these new methods avoid the use of Lyapunov variables, which gives them two major strategic advances over matrix inequality methods. Due to the much smaller number of decision variables, they do not suffer from size restrictions, and they are much easier to adapt to structural constraints on the controller. In this paper, we further develop this line and address both frequency- and time-domain design specifications by means of a nonsmooth algorithm general enough to handle both cases. Numerical experiments are presented for reliable or fault-tolerant control, and for time response shaping.     

Robust H∞ control for linear discrete-time systems with norm-bounded time-varying uncertainty

The problem of robust H_∞ analysis and synthesis for linear discrete-time systems with norm-bounded time-varying uncertainty is studied in this paper. It will be shown that this problem is equivalent to the problem of H_∞ analysis and synthesis of an auxiliary system. The necessary and sufficient conditions for the equivalency are proved. Thus the original problem can be solved by existing H_∞ control methods.