invariant region preserving dg methods for multi dimensional hyperbolic conservation law systems with an application to compressible euler equations abstract an invariant region preserving irp limiter for multi dimensional hyperbolic conservation law systems is introduced as long as the system admits a global invariant region which is a convex set in the phase space it is shown that the order of approximation accuracy is not destroyed by the irp limiter provided the cell average is away from the boundary of the convex set moreover this limiter is explicit and easy for computer implementation a generic algorithm incorporating the irp limiter is presented for high order finite volume type schemes for arbitrarily high order discontinuous galerkin dg schemes to hyperbolic conservation law systems sufficient conditions are obtained for cell averages to remain in the invariant region provided the projected one dimensional system shares the same invariant region as the full multi dimensional hyperbolic system does the general results are then applied to both one and two dimensional compressible euler equations so to obtain high order irp dg schemes numerical experiments are provided to validate the proven properties of the irp limiter and the performance of irp dg schemes for compressible euler equations

composite quadratic lyapunov functions for constrained control systems a lyapunov function based on a set of quadratic functions is introduced in this paper we call this lyapunov function a composite quadratic function some important properties of this lyapunov function are revealed we show that this function is continuously differentiable and its level set is the convex hull of a set of ellipsoids these results are used to study the set invariance properties of continuous time linear systems with input and state constraints we show that for a system under a given saturated linear feedback the convex hull of a set of invariant ellipsoids is also invariant if each ellipsoid in a set can be made invariant with a bounded control of the saturating actuators then their convex hull can also be made invariant by the same actuators for a set of ellipsoids each invariant under a separate saturated linear feedback we also present a method for constructing a nonlinear continuous feedback law which makes their convex hull invariant

output feedback control of saturated discrete time linear systems using parameter dependent lyapunov functions in this paper we present a new output feedback control approach for discrete time linear systems subject to actuator saturations using parameter dependent lyapunov functions the saturation level indicator serves as a scheduling parameter the resulting nonlinear controller is expressed in a quasi lpv linear parameter varying form and the stabilization and disturbance attenuation problems are formulated and solved as finite dimensional linear matrix inequality lmi optimization problems our approach is less conservative than a single quadratic lyapunov function method specifically the proposed output feedback control law asymptotically stabilizes the open loop system with a larger domain of attraction and achieves better disturbance attenuation under energy and magnitude bounded disturbances

lmi based stability analysis for fuzzy model based control systems using artificial t s fuzzy model this paper investigates the stability of fuzzy model based fmb control systems an alternative stability analysis approach using an artificial fuzzy system based on the lyapunov stability theory is proposed to facilitate the stability analysis the continuous membership functions of the takagi sugeno t s fuzzy model are represented by the staircase ones with the nice property of the staircase membership functions it turns the set of infinite number of linear matrix inequality lmi based stability conditions into a finite one furthermore the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions the stability of the original fmb control systems is guaranteed by the satisfaction of the lmi based stability conditions the proposed stability analysis is applied to the fmb control systems of which the t s fuzzy model and fuzzy controller do not share the same premise membership functions and thus is able to enhance the design flexibility of the fuzzy controller a simulation example is given to illustrate the merits of the proposed approach

model construction rule reduction and robust compensation for generalized form of takagi sugeno fuzzy systems this paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction rule reduction and robust compensation for nonlinear systems the model construction part replaces the nonlinear dynamics of a system with a generalized form of takagi sugeno fuzzy systems which is newly developed by us the generalized form has a decomposed structure for each element of a sub i and b sub i matrices in consequent parts the key feature of this structure is that it is suitable for constructing if then rules and reducing the number of if then rules the rule reduction part provides a successive procedure to reduce the number of if then rules furthermore we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models the robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties finally two examples demonstrate the utility of the systematic procedure developed

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

simulating alternating tree automata by nondeterministic automata new results and new proofs of the theorems of rabin mcnaughton and safra abstract we give a proof that alternating tree automata can be simulated by nondeterministic tree automata which yields new complexity results and a unified proof of the theorems of rabin mcnaughton and safra we also give a simple axiomatic framework for uniformizing strategies

sampled data observer based output feedback fuzzy stabilization of nonlinear systems exact discrete time design approach this paper presents a new direct discrete time design methodology of a sampled data observer based output feedback fuzzy controller for a class of nonlinear system that is exactly modeled in takagi sugeno s form at least locally a fundamental yet challenging issue in this direction is the unavailability of the exact discrete time model of the nonlinear plant in a closed form in contrast to the earlier works that are based on an approximate discrete time model thus the stability obtained in the design step is not preserved in the implementation step we employ an exact discrete time fuzzy model in an integral form sufficient asymptotic stabilization conditions are investigated in the discrete time lyapunov sense we then show that the resulting sampled data controller indeed asymptotically stabilizes the nonlinear plant an example is provided to illustrate the effectiveness of the proposed methodology

short communication on balancing a cart pole system using t s fuzzy model this paper presents two easily implementable control schemes for balancing a cart pole system using intelligent control tools the proposed schemes use the takagi sugeno t s fuzzy model of a nonlinear system the concept of network inversion is used to design the controller for such a system in one of the control schemes the control input necessary to achieve a desired output is computed directly through iterative inversion of the fuzzy model in the other scheme a parallel distributed compensator form is chosen for the controller and the parameters or the feedback gains of the controller are updated through network inversion the updating laws are derived using both continuous and discrete time lyapunov approaches the inversion based parameter update avoids the need of any sufficient condition or prerequisite constraint as in existing t s fuzzy model based control designs like lmi techniques and robust control techniques the proposed controllers have been implemented on the cart pole system both in simulation and real time a comparative performance analysis for different control algorithms is presented the performance of the proposed controller is compared with the well established lqr control in real time the proposed control algorithms work for a wide range of operating regions compared to lqr and are more robust in the sense that they can tolerate an output disturbance of higher magnitude

fuzzy dynamic output feedback control through nonlinear takagi sugeno models we present a convex way to design a fuzzy dynamic output feedback compensator for locally stabilizing a class of nonlinear discrete time systems this class consists of the systems described by takagi sugeno t s models with a sector bounded nonlinear additive term and saturated control signals the local stabilization takes into account the domain of validity of these t s models which is a key issue for practical applications two types of nonlinear fuzzy compensators are considered one having all matrices of the controller depending on fuzzy grade membership functions and the other with only a subset of the matrices with such a dependency the controller design includes a fuzzy anti windup gain that handles saturating actuators besides a time performance index based on the contractivity of the level set of the fuzzy lyapunov function is proposed regarding the closed loop system examples are given to illustrate the effectiveness of this proposal

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

optimal control of markov decision processes with linear temporal logic constraints in this paper we develop a method to automatically generate a control policy for a dynamical system modeled as a markov decision process mdp the control specification is given as a linear temporal logic ltl formula over a set of propositions defined on the states of the mdp motivated by robotic applications requiring persistent tasks such as environmental monitoring and data gathering we synthesize a control policy that minimizes the expected cost between satisfying instances of a particular proposition over all policies that maximize the probability of satisfying the given ltl specification our approach is based on the definition of a novel optimization problem that extends the existing average cost per stage problem we propose a sufficient condition for a policy to be optimal and develop a dynamic programming algorithm that synthesizes a policy that is optimal for a set of ltl specifications

reduced order dynamic output feedback control of continuous time t s fuzzy systems the problem of reduced order dynamic output feedback control design for continuous time takagi sugeno fuzzy systems with h guaranteed cost is addressed the proposed approach is based on a line integral fuzzy lyapunov function with arbitrary polynomial dependence on the premise variables allowing the membership functions modeled as multi simplexes to vary arbitrarily the controller is obtained by transforming the problem into a static output feedback control design problem solved by means of a two stages linear matrix inequality procedure the main appeal of the approach is that the order of the output feedback controller as well as the dependence of the premise variables are customizable for control implementation purposes examples illustrate the flexibility of the method and also that the proposed strategy can provide less conservative results when compared to other methods for full order dynamic output feedback controllers from the literature of continuous time takagi sugeno fuzzy systems

experiments with deterministic ω automata for formulas of linear temporal logic this paper addresses the problem of generating deterministic automata for formulas of linear temporal logic which can be solved by applying well known algorithms to construct a nondeterministic buchi automaton for the given formula on which we then apply a determinization algorithm we study here in detail safra s determinization algorithm present several heuristics that attempt to decrease the size of the resulting automata and report on experimental results

non quadratic local stabilization for continuous time takagi sugeno models this paper is concerned with non quadratic stabilization of continuous time takagi sugeno ts models the well known problem of handling time derivatives of membership functions mfs as to obtain conditions in the form of linear matrix inequalities lmis is overcome by reducing global goals to the estimation of a region of attraction instead of parallel distributed compensation pdc a non pdc control law is proposed according to the non quadratic nature of the lyapunov function examples are provided to show the advantages over the quadratic and some non quadratic approaches

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

brief circle and popov criteria as tools for nonlinear feedback design we convert classical absolute stability criteria into nonlinear design procedures which employ efficient numerical tools such as lmi s we first analyze an earlier circle criterion design and show that its feasibility is limited by conditions on the unstable part of the zero dynamics and the relative degree then we develop an extended circle criterion design which eliminates the relative degree obstacle the restrictions on the zero dynamics are relaxed by using the popov multiplier which also reduces controller complexity the results are illustrated with several design examples

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

a unified translation of linear temporal logic to ω automata we present a unified translation of ltl formulas into nondeterministic buchi automata limit deterministic buchi automata ldba and deterministic rabin automata dra the translations yield automata of asymptotically optimal size double or single exponential respectively all three translations are derived from one single master theorem of purely logical nature the master theorem decomposes the language of a formula into a positive boolean combination of languages that can be translated into automata by elementary means all three translations are direct and no intermediate constructions are used

antiwindup design with guaranteed regions of stability an lmi based approach this note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs considering that a linear dynamic output feedback has been designed to stabilize the linear system without saturation a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed loop system it is shown that the closed loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity a modified sector condition is then used to obtain stability conditions based on quadratic lyapunov functions differently from previous works these conditions are directly in linear matrix inequality form some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones

gain scheduled output control design for a class of discrete time nonlinear systems with saturating actuators this paper deals with the stabilization of a class of nonlinear discrete time systems under control saturations including time varying parameter dependency the control law studied consists of the gain scheduled feedback of the measured output and of the nonlinearity present in the dynamics of the controlled system furthermore the saturations are taken into account by modeling the nonlinear saturated system through a dead zone nonlinearity satisfying a modified sector condition thus as for precisely known systems linear matrix inequality lmi stabilization conditions are proposed for such a generic system these conditions can be cast into convex programming problems for design purposes an illustrative example stresses the efficiency of the main result

method for higher order polynomial sugeno fuzzy inference systems a method for higher order polynomial sugeno fuzzy inference systems formation is presented compared to other existing higher order sugeno implementations it uses fewer parameters and compared to zero and 1st order sugeno fuzzy systems it has overall improved model performance while best models are not always obtained via a higher order representation in our proposed method it is possible to choose the polynomial order which best fits the desired data its input is a previously established model found by a clustering algorithm subtractive algorithm in this case afterward parameters of all higher order polynomials are adjusted using recursive least square algorithm for experimental validation multiple benchmark datasets are tested using hold out and k fold validation as well as data forecasting various performance measures are used although akaike information criterion is used as a primary measure to demonstrate that our proposed higher order polynomials have overall better model performance over zero and 1st order polynomials

minimal counterexamples for linear time probabilistic verification abstract counterexamples for property violations have a number of important applications like supporting the debugging of erroneous systems and verifying large systems via counterexample guided abstraction refinement in this paper we propose the usage of minimal critical subsystems of discrete time markov chains and markov decision processes as counterexamples for violated regular properties minimality can thereby be defined in terms of the number of states or transitions this problem is known to be np complete for markov decision processes we show how to compute such subsystems using mixed integer linear programming and evaluate the practical applicability in a number of experiments they show that our method yields substantially smaller counterexample than using existing techniques

fair simulation relations parity games and state space reduction for buchi automata we give efficient algorithms improving optimal known bounds for computing a variety of simulation relations on the state space of a buchi automaton our algorithms are derived via a unified and simple parity game framework this framework incorporates previously studied notions like fair and direct simulation but also a new natural notion of simulation called delayed simulation which we introduce for the purpose of state space reduction we show that delayed simulation unlike fair simulation preserves the automaton language upon quotienting and allows substantially better state space reduction than direct simulation using our parity game approach which relies on an algorithm by jurdzinski we give efficient algorithms for computing all of the above simulations in particular we obtain an o mn3 time and o mn space algorithm for computing both the delayed and the fair simulation relations the best prior algorithm for fair simulation requires time and space o n6 our framework also allows one to compute bisimulations we compute the fair bisimulation relation in o mn3 time and o mn space whereas the best prior algorithm for fair bisimulation requires time and space o n10