Logarithmic integrals, interpolation bounds, and performancelimitations in MIMO feedback systems

We study performance limitation issues found in linear multivariable feedback systems. Our main contributions include Bode and Poisson type integral inequalities and performance limits for the sensitivity and complementary sensitivity functions. These results characterize and quantify explicitly how open-loop unstable poles and nonminimum phase zeros may impose inherent limitations on feedback design and fundamental limits on the best achievable performance. The role of time delay is also studied in this context. Most notably, we show that the performance and design limitations in multivariable systems intrinsically depend on the locations as well as directions of unstable poles and nonminimum phase zeros, and in particular, on how pole and zero directions are aligned. The latter is characterized by angles measuring the mutual orientation between zero and pole directions, and it is shown to play a crucial role in multivariable system design     

A Robust Model Control for Dynamic Systems

Analytical methods of polynomial algebra, heuristic techniques, and digital modeling are used to study the robustness domain of linear dynamic systems with model input–output controllers as a function of the mutual locations of zeros and poles of the transfer function of the controlled object and poles of the characteristic polynomial. Conditions for parametric robustness are determined. A method of choosing the measured output coordinate of the automatic control system during structure formation from optimal-speed requirements is described.     

Robustness analysis via the running time of the interior point methods

Let Σ be the set of stable linear time-invariant autonomous systems, equipped with a stability robustness measure ρ. Let be the measure of the computational efficiency of the algorithm that verifies the stability of the elements of Σ. We demonstrate the existence of a robustness measure ρ, algorithm , and a monotonically increasing function h, such that for all stable ,implications of this relationship are then discussed.     

I — an interactive program for calibrating activated sludge systems

I — an interactive program for calibrating activated sludge systems is formulated and demonstrated. The model involves a heuristic screening algorithm for exploring the system equations structure, analytical computations of the sensitivities of the variables to the model coefficients, analytical computations of the gradients of the objective functions selected for the calibration process, and a gradient interactive steepest descent minimization scheme. The methodology was implemented in an end-user PC program: I , that uses the TK S ® and M ® as computational engines, and as the shell. Applications to the activated sludge system models of (Argaman Water Research 29(1) and Argaman et al. (Journal of Environmental Engineering ASCE 125(7) (1999), 608-617) are presented.     

A Resolution-based Model Building Algorithm for a Fragment of =: (Extended Abstract)

1 [11] is a decidable subclass of first-order clausal logic without equality. [7] shows that 1 becomes undecidable when equational literals are allowed, but remains decidable if equality is restricted to ground terms only.First, we extend this decidability result to some non ground equational literals. By carefully restricting the use of the equality predicate we obtain a new decidable class, called 1 ₌^*. We show that existing paramodulation calculi do not terminate on 1 ₌^* and we define a new simplification rule which allows to ensure termination. Second, we show that the automatic extraction of Herbrand models is possible from saturated sets in 1 ₌^* not containing □. These models are represented by certain finite sets of (possibly equational and non ground) linear atoms. The difficult point here is to show that this formalism is suitable as a model representation mechanism, i.e. that the evaluation of arbitrary non equational first-order formulae in such interpretations is a decidable problem.     

Formulas relating stability estimates of discrete-time and sampled-data nonlinear systems

We provide an explicit stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the estimate for the corresponding discrete-time system and a function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system. Our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results in [[Reference to 1]] or extend some results in [[Reference to 4]] to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate.     

Properties of optimal weighted sensitivity designs

Weighted sensitivity designs for a class of single-input/single-output, linear time-invariant systems are shown to have the property that the optimal controller has fewer right-half plane poles than the plant has right-half plane zeros. While weighted complementary sensitivity designs are shown to have the property that the optimal controller has fewer right-half plane zeros than the plant has right-half plane poles. Effects of various choices of weighting functions on the optimal solutions are described     

Matrix-theoretic conditions for the realizability of sliding manifolds

Systems of the type , , where sgn(·) is the vector sign function, usually determine the realizability of sliding modes in control systems with high-frequency gain K. A new condition on K is established for the global stability of this system using a nonsmooth Liapunov function. This condition is used to establish necessary and sufficient stability conditions for second-order systems.     

Fuzzy output feedback control of nonlinear systems under sampled measurements

This paper studies the problem of designing an fuzzy feedback control for a class of nonlinear systems described by a continuous-time fuzzy system model under sampled output measurements. The premise variables of the fuzzy system model are allowed to be unavailable. We develop a technique for designing an fuzzy feedback control that guarantees the gain from an exogenous input to a controlled output is less than or equal to a prescribed value. A design algorithm for constructing the fuzzy feedback controller is given.     

Implementing Compositional Analysis Using Intersection Types With Expansion Variables

A program analysis is compositional when the analysis result for a particular program fragment is obtained solely from the results for its immediate subfragments via some composition operator. This means the subfragments can be analyzed independently in any order. Many commonly used program analysis techniques (in particular, most abstract interpretations and most uses of the Hindley/Milner type system) are not compositional and require the entire text of a program for sound and complete analysis.System is a recent type system for the pure λ-calculus with intersection types and the new technology of expansion variables. System supports compositional analysis because it has the principal typings property and an algorithm based on the new technology of β-unification has been developed that finds these principal typings. In addition, for each natural number k, typability in the rank-k restriction of System is decidable, so a complete and terminating analysis algorithm exists for the rank-k restriction.This paper presents new understanding that has been gained from working with multiple implementations of System and β-unification-based analysis algorithms. The previous literature on System presented the type system in a way that helped in proving its more important theoretical properties, but was not as easy to follow as it could be. This paper provides a presentation of many aspects of System that should be clearer as well as a discussion of important implementation issues.     

Formative Processes with Applications to the Decision Problem in Set Theory: I. Powerset and Singleton Operators

This paper introduces formative processes, composed by transitive partitions. Given a family of sets, a formative process ending in the Venn partition Σ of is shown to exist. Sufficient criteria are also singled out for a transitive partition to model (via a function from set variables to unions of sets in the partition) all set-literals modeled by Σ. On the basis of such criteria a procedure is designed that mimics a given formative process by another where sets have finite rank bounded by C(|Σ|), with C a specific computable function. As a by-product, one of the core results on decidability in computable set theory is rediscovered, namely the one that regards the satisfiability of unquantified set-theoretic formulae involving Boolean operators, the singleton-former, and the powerset operator. The method described (which is able to exhibit a set-solution when the answer is affirmative) can be extended to solve the satisfiability problem for broader fragments of set theory.     

The Solution Operator of the Korteweg-de Vries Equation is Computable

The initial value problem of the Korteweg-de Vries (KdV) equation posted on the real line R: defines a nonlinear map K from the space H^s( ) to the space C( , H^s( )) for any given real numbers s ≥ = 0. In this paper we prove that the map K_R is computable for any integer s ≥ = 3.     

A family of maximal noncontrollable Lie wedges with empty interior

Let S_k be the semigroup of matrices in having nonnegative k-minors. Its Lie wedge generates and is noncontrollable. It is proved here that is a maximal noncontrollable Lie wedge if k=1, n−1 or when k and n are even. The latter is the family of Lie wedges mentioned in the title.     

Automatic verification of a manufacturing system

Due to increasing complexity and costs involved, powerful techniques are needed to analyse manufacturing systems. In order to improve these techniques, which are often based on simulation, our research focuses on application of formal methods to manufacturing systems. We translate a simulation model into a format suitable for model checking. The advantage of model checking, as opposed to simulation, is that we can prove liveness, eventually something good will happen, and safety, something bad will never happen, properties of manufacturing systems. We applied our approach to a model of a manufacturing system consisting of a turntable, a drill, and a testing device. The model was written in the χ language, which has been used extensively to simulate large manufacturing systems. We translated the model into , the input language of the popular model checker . After that, we used to verify that the model does not have deadlock and that it makes progress under all circumstances.     

Inclusion of Zeros of Nowhere Differentiable n-Dimensional Functions

A method is described for calculating verified error bounds for zeros of a system of nonlinear equations f(x) = 0 with continuous f : R" R". We do not require existence of partial derivatives of f, and the function f may even be known only up to some finite precision > 0.An inclusion may contain infinitely many zeros of f. An example of a continuous but nowhere differentiable function is given.     

Design of optimal reduced order filters

This paper shows that the design of a reduced order optimal filter is equivalent to a frequency weighted norm model reduction problem.     

Extracting models from clause sets saturated under semantic refinements of the resolution rule

We present an algorithm that—given a set of clauses S saturated under some semantic refinements of the resolution calculus—automatically constructs a Herbrand model of S. is represented by a set of atoms with equality and disequality constraints interpreted over the finite tree algebra, hence the problem of evaluating first-order formulae in is decidable.     

Lie algebraic methods in optimal control of stochastic systems with exponential-of-integral cost

The purpose of this paper is to formulate and study the optimal control of partially observed stochastic systems with exponential-of-integral-sample cost, known as risk-sensitive problems, using Lie algebraic tools. This leads to the introduction of the sufficient statistic algebra, , through which one can determine á priori the maximum order of the controller. When , the construction of the control laws is addressed through extensions of the Wei–Norman method, as in nonlinear filtering problems. Aside from specific known finite-dimensional examples which are studied in order to delineate the application of the Lie algebraic tools, new classes of finite-dimensional controllers are identified as well. In addition, relations with minimax dynamic games are explored to best assess the importance and generality of the finite-dimensional control systems.     

Notes on the definition of behavioural controllability

We take another look at the behavioural definition of controllability for discrete one-dimensional (1D) systems, and its extension to multidimensional (nD) systems defined on or . We suggest that the current definition for nD systems is inappropriate for systems defined on the domain , and that care has to be taken even with the 1D definition. We propose a new definition which applies to all standard classes of discrete nD systems.