Funnel control for fully actuated systems under a fragment of signal temporal logic specifications

Temporal logics have lately proven to be a valuable tool for various control applications by providing a rich specification language. Existing temporal logic-based control strategies discretize the underlying dynamical system in space and/or time. We will not use such an abstraction and consider continuous-time systems under a fragment of signal temporal logic specifications by using the associated robust semantics. In particular, this paper provides computationally-efficient funnel-based feedback control laws for a class of systems that are, in a sense, feedback equivalent to single integrator systems, but where the dynamics are partially unknown for the control design so that some degree of robustness is obtained. We first leverage the transient properties of a funnel-based feedback control strategy to maximize the robust semantics of some atomic temporal logic formulas. We then guarantee the satisfaction for specifications consisting of conjunctions of such atomic temporal logic formulas with overlapping time intervals by a suitable switched control system. The result is a framework that satisfies temporal logic specifications with a user-defined robustness when the specification is satisfiable. When the specification is not satisfiable, a least violating solution can be found. The theoretical findings are demonstrated in simulations of the nonlinear Lotka–Volterra equations for predator–prey models.     

Stable fuzzy logic design of point-to-point control for mechanical systems

An approach for the development of fuzzy point-to-point control laws for second-order mechanical systems is presented. Asymptotic stability of the resulting closed-loop system is proved using Lyapunov stability theory. Closed-loop performance and robustness are quantified in terms of the parameters of membership functions. As opposed to most existing fuzzy control laws, the closed-loop stability of the proposed controller does not depend on the knowledge of the entire dynamics. Moreover, the approach does not require the plant to be open-loop stable. The proposed approach is demonstrated on design and simulation study of a fuzzy controller for a two-link robotic arm.     

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study.     

On temporal logic S4Dbr

In this paper, we study the temporal logic S4Dbr with two temporal operators “always” and “eventually.” An equivalent sequent calculus is presented with formulae as modal clauses or modal clauses starting with operator “always.” An upper bound of deduction tree is given for propositional logic. A theorem prover for propositional logic is written in SWI-Prolog. Published in LietuvosMatematikos Rinkinys, Vol. 46, No. 2, pp. 203–214, April–June, 2006.     

Proof-theoretical investigation of temporal logic with time gaps

In the paper, the first-order intuitionistic temporal logic sequent calculus LBJ is considered. The invertibility of some of the LBJ rules, syntactic admissibility of the structural rules and the cut rule in LBJ, as well as Harrop and Craig's interpolation theorems for LBJ are proved. Gentzen's midsequent theorem is proved for the LBJ' calculus which is obtained from LBJ by removing the antecedent disjunction rule from it. Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 255–276, July–September, 2000.     

A note on unbounded metric temporal logic over dense time domains

We investigate the consequences of removing the infinitary axiom and rules from a previously defined proof system for a fragment of propositional metric temporal logic over dense time (see [1]). (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Past–future separation and normal forms in temporal predicate logic specifications

Temporal specifications are often used when phenomena are modelled where dynamics play a main role. If simulation is one of the aims of modelling, usually a restricted, executable modelling language format is used, based on some form of past to future implications. In this paper a detailed transformation procedure is described that takes any temporal predicate logic specification and generates a specification in a past-implies-future normal format. The procedure works for temporal specifications in which the atoms either express time ordering relations or are state-related, i.e., include only one time variable.     

Infinitary calculus for a restricted first-order linear temporal logic without contraction on quantified formulas

An infinitary calculus for a restricted fragment of the first-order linear temporal logic is considered. We prove that for this fragment one can construct the infinitary calculusG _Lω ^* without contraction on predicate formulas. The calculusG _Lω ^* possesses the following properties: (1) the succedent rule for the existential quantifier is included into the corresponding axiom; (2) the premise of the antecedent rule for the universal quantifier does not contain a duplicate of the main formula. The soundness and completness ofG _Lω ^* are also proved. Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 378–397, July–September, 1999. Translated by R. Lapinskas     

Fuzzy logic in commercial expert systems — Results and prospects

This paper surveys the use of fuzzy methods in commercial applications of the technology of expert systems and in commercial products which aim to support such applications. It attempts to evaluate the utility of such an approach to uncertainty management compared to other well known methods of handling uncertainty in expert systems. Starting from this base it attempts an evaluation of the prospects for fuzzy expert systems in the medium term. As a survey it attempts to list applications and commercial products as comprehensively as is practical and includes an extensive bibliography on the topic.     

L2-stabilization design for fuzzy control systems

System's stability is the most important requirement in control system designs. Fuzzy control system (FCS) should satisfy this requirement also. This paper shows that a linear plant with the formulated Fuzzy Logic Controller (FLC) is a nonlinear system and its stability can be analyzed by applying the Small Gain Theorem or the Circle Criterion. By these two criteria, three FLC design procedures are introduced to guarantee the stabilization of the FCS. Finally, two examples are given to confirm the availability of the proposed design approaches.     

A dynamical systems result on asymptotic integration of linear differential systems

We are interested in the asymptotic integration of linear differential systems of the form x′=[Λ(t)+R(t)]x, where Λ is diagonal and R∈L^p[t₀,∞) for p∈[1,2]. Our dichotomy condition is in terms of the spectrum of the omega-limit set ω_Λ. Our results include examples that are not covered by the Hartman-Wintner theorem.     

Approximation with the output of linear control systems

In this paper we give a new proof that for controllable and observable linear systems every L²[0,T] function can be approximated in the L²[0,T] sense with an output function generated by an L²[0,T] input function. We also give a new characterization of how continuous functions on [0,T] are uniformly approximated by an output generated by a continuous input function. The relative degree of the transfer function of the system determines those functions that can be approximated. We further show that if the initial data is allowed to vary then every continuous function is uniformly approximated by outputs generated by continuous functions.     

A control parametrization algorithm for optimal control problems involving linear systems and linear 1

Computational schemes based on control parametrization techniques are known to be very efficient for solving optimal control problems. However, the convergence result is only available for the case in which the dynamic system is linear and without the terminal equality and inequality constraints. This paper is to improve this convergence result by allowing the presence of the linear terminal inequality. For illustration, an example arising in the study of optimally one-sided heating of a metal slab in a furnace is considered.     

Local computation in linear logic

This work deals with the exponential fragment of Girard's linear logic ([3]) without the contraction rule, a logical system which has a natural relation with the direct logic ([10], [7]). A new sequent calculus for this logic is presented in order to remove the weakening rule and recover its behavior via a special treatment of the propositional constants, so that the process of cut-elimination can be performed using only “local” reductions. Hence a typed calculus, which admits only local rewriting rules, can be introduced in a natural manner. Its main properties — normalizability and confluence — has been investigated; moreover this calculus has been proved to satisfy a Curry-Howard isomorphism ([6]) with respect to the logical system in question. MSC: 03B40, 03F05.     

The Betti reciprocity principle and the normal boundary component control problem for linear elastic systems

The background for this article is the question of modification of the geometric configuration of an elastic structure by means of “volume” type actuation. In this actuation mode stresses are applied to the elastic body by injection/extraction of a fluid into, or from, a large number of vacuoles in the elastic “matrix” material. Previous articles by the author, and others, have examined this process and studied its effectiveness in the context of a “naive” continuous model. The present paper continues along these lines, exploring “normal boundary component controllability” criterion for determining achievable configurations for the controlled system in the two-dimensional case. Connections with conformal mapping lead to affirmative results for approximate controllability in this sense and Fourier series techniques provide exact controllability results for the case wherein the domain of the uncontrolled system is a two-dimensional disk.      

Analyzing completeness of axiomatic functional systems for temporal × modal logics

In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties ofthe accessibility functions (being injective, surjective, increasing, etc.) have been considered and axiomatic systems (called functional) which define these properties have been given. Only a few ofthese systems have been proved tobe complete. The aim ofthis paper is to make a progress in the study ofcompleteness for functional systems. For this end, we use indexes as names for temporal flows and give new proofs of completeness. Specifically, we focus our attention on the system which defines injectivity, because the system which defines this property without using indexes was proved to be incomplete in previous works. The only system considered which remains incomplete is the one which defines surjectivity, even ifwe consider a sequence ofnatural extensions ofthe previous one (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of characteristic delays in multivariable control systems wcbsl

Pure time delays in multivariable control systems place severe restrictions on achievable feedback performance. This paper considers an approach to modelling distributed time-delay systems using discrete convolution. The basis for convolution algebra is briefly outlined and the new concepts of characteristic pattern and vector delays are introduced. A process control example is given that illustrates the concepts and shows typical results obtained using WCBSL (Windows Convolution-Based Simulation Language)     

Autonomous control of complex systems: robotic applications

One of the biggest challenges of any control paradigm is being able to handle large complex systems under unforeseen uncertainties. A system may be called complex here if its dimension (order) is too high and its model (if available) is nonlinear, interconnected, and information on the system is uncertain such that classical techniques cannot easily handle the problem. Soft computing, a collection of fuzzy logic, neuro-computing, genetic algorithms and genetic programming, has proven to be a powerful tool for adding autonomy to many complex systems. For such systems the size soft computing control architecture will be nearly infinite. Examples of complex systems are power networks, national air traffic control system, an integrated manufacturing plant, etc. In this paper a new rule base reduction approach is suggested to manage large inference engines. Notions of rule hierarchy and sensor data fusion are introduced and combined to achieve desirable goals. New paradigms using soft computing approaches are utilized to design autonomous controllers for a number of robotic applications at the ACE Center are also presented briefly.