Branicky, M. S., Borkar, V. S., and Mitter, S. K. (1998). A unified framework for hybrid control: Model and optimal theory. IEEE Trans. Automatic Control 43 (1), 31--45.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....that has access to a quantized version of the linear system s output is considered. This approach suffers from spurious solutions that must be trimmed from the automaton behavior. Hybrid optimal control problems have been studied in papers by Witsenhausen [tt] and Branicky, Borkar, Mitter [3]. These studies concentrate on problems of well posedness, necessary conditions, and existence of optimal solutions but do not provide algorithmic solutions. 2 Optimal control problem Notation. 1( is the indicator function. cl(A) denotes the closure of set A. I1 II denotes the Euclidean norm. ....

M. Branicky, V. Borkar, S. Mitter. A unified framework for hybrid control: model and optimal control theory. IEEE Trans. AC, vol. 43, no. 1, pp. 31-45, January, 1998.

....namely, general switched linear quadratic (GSLQ) problems where each subsystem is linear and the cost functionals are in general quadratic forms. However, theoretical or practical results for optimal control of switched systems with state jumps have rarely be reported in the literature (see e.g. [2, 3, 4, 5, 8]; 3, 4] deal with autonomous switched systems and [2, 5, 8] propose some theoretical results) In such problems, the discontinuities of the system states at the switching instants pose additional di#culties. In this paper, we extend the approach in [13] to GSLQ problems with state jumps. Since ....

....subsystem is linear and the cost functionals are in general quadratic forms. However, theoretical or practical results for optimal control of switched systems with state jumps have rarely be reported in the literature (see e.g. 2, 3, 4, 5, 8] 3, 4] deal with autonomous switched systems and [2, 5, 8] propose some theoretical results) In such problems, the discontinuities of the system states at the switching instants pose additional di#culties. In this paper, we extend the approach in [13] to GSLQ problems with state jumps. Since many practical problems only involve optimization where the ....

[Article contains additional citation context not shown here]

M. S. Branicky, V. S. Borkar, S. K. Mitter, "A unified framework for hybrid control: model and optimal control theory," IEEE Trans. on Auto. Contr. 43(1), pp. 31-45, January, 1998.

....via one of a set of pre defined regulators. The higher level, the supervisor, monitors the behavior of the plant and intervenes when its state enters a set of boundary states. Intervention takes the form of switching to a new low level regulator. This is not unlike many hybrid control methods [8] except that the low level process is formalized as a finite MDP and the supervisor s task as a finite SMDP. The supervisor s decisions occur whenever the plant reaches a boundary state, which e#ectively erases the intervening states from the supervisor s decision problem, thereby reducing its ....

M. S. Branicky, V. S. Borkar, and S. K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Transactions on Automatic Control, 43:31=45, 1998.

....systems, air and ground traffic management systems, sequential operations and safety interlock systems in chemical processes, etc. Beyond this rather general definition extends an extensive taxonomy of models that have been proposed in recent years for the description of hybrid systems (e.g. see [7]) Indeed, it is difficult to make progress without appealing to some form of model formulation. Somewhat confusingly, a hybrid system may also be either continuous time or discrete time. For example, discrete time formulations have recently been employed in the design of model predictive ....

M. S. Branicky, V. S. Borkar, and S. K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Transactions on Automatic Control, 43(1):31--45, 1998.

....it makes sense to think of the old current control a(t )attimet as part of an augmented state vector y aug (t) y(t) a(t ) at time t. This can be done formally by including a(t ) as part of the state vector, in which case a switching control problem becomes an impulse control problem (see [10], where problems of this sort are set in the general framework of hybrid systems) We shall keep the switchingcontrol formalism here; however, in implementing optimization algorithms, we shall see that it is natural to consider augmented state feedback controls (x, a j ) # a(x, a j ) rather ....

M.S. Branicky, V.S. Borkar and S.K. Mitter, A unified framework for hybrid control: Model and optimal control theory, IEEE Trans. Automat. Contr. 43 (1998), 31-45.

.... Petri nets (see [1] Broadly speaking, two categories of modeling frameworks have been proposed to study hybrid systems: Those that extend event driven models to include time driven dynamics# and those that extend the traditional time models to include event driven dynamics # for an overview, see [2,3,4]. The hybrid system modeling framework considered in this paper falls into the first category above. It is largely motivated by the structure of manymanufacturing systems. In these systems, discrete entities (referred to as jobs)move through a network of workcenters which process the jobs so as ....

M.S. Branicky, V.S. Borkar and S.K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Trans. on Automatic Control, 43:31--45, Jan., 1998.

....discrete jumps. Hybrid systems have been a topic of great interest, primarily in the control and computer theory communities. Motivated by applications to avionics, hardware and real time software verification, transportation systems, and manufacturing, methods for modeling [LSVW96, AH97, vS98, BBM98, JELS99] analyzing [Bra98, YMH98, JR98, ACH 95, HKPV98, LPS00] and controlling [MPS95, BM97, BBM98, LTS99] hybrid systems have been proposed. In this paper we present a geometric approach for treatment of a class of hybrid systems which resemble deterministic continuous time dynamical ....

....theory communities. Motivated by applications to avionics, hardware and real time software verification, transportation systems, and manufacturing, methods for modeling [LSVW96, AH97, vS98, BBM98, JELS99] analyzing [Bra98, YMH98, JR98, ACH 95, HKPV98, LPS00] and controlling [MPS95, BM97, BBM98, LTS99] hybrid systems have been proposed. In this paper we present a geometric approach for treatment of a class of hybrid systems which resemble deterministic continuous time dynamical systems. Early results in this direction where first reported in [SJSL00] We introduce the notions of the ....

Michael S. Branicky, Vivek S. Borkar, and Sanjoy K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Transactions on Automatic Control, 43(1):31--45, 1998.

....with instanteneous, discrete jumps. Hybrid systems have been a topic of great interest, primarily in the control and computer theory communities. Motivated by applications to avionics, hardware and real time software verification, transportation systems and manufacturing, methods for modeling [1, 2, 3, 4, 5], analysing [6, 7, 8, 9, 10, 11] and controlling [12, 13, 4, 14] hybrid systems have been proposed. In this paper we present a geometric approach for treatment of a class of hybrid systems which resemble deterministic dynamical systems. Early results in this direction where first This work was ....

....a topic of great interest, primarily in the control and computer theory communities. Motivated by applications to avionics, hardware and real time software verification, transportation systems and manufacturing, methods for modeling [1, 2, 3, 4, 5] analysing [6, 7, 8, 9, 10, 11] and controlling [12, 13, 4, 14] hybrid systems have been proposed. In this paper we present a geometric approach for treatment of a class of hybrid systems which resemble deterministic dynamical systems. Early results in this direction where first This work was supported by the NASA grant NAG 2 1039, the Swedish Foundation for ....

M. S. Branicky, V. S. Borkar, and S. K. Mitter, "A unified framework for hybrid control: Model and optimal control theory," IEEE Transactions on Automatic Control, vol. 43, no. 1, pp. 31--45, 1998.

....of the maps from the output measurements to control inputs, so that small changes in the input cause small changes in the output. In [NER 93a] these topological issues are studied for hybrid systems and small topologies are introduced for the design of the analog to digital map. In [BRA 94] BRA 98a] a unified hybrid systems model is introduced, which captures many discrete phenomena arising in hybrid systems. These phenomena include autonomous switchings, which refer to the discontinuous changes of the vector field describing the dynamics of the system when the state hits certain ....

BRANICKY M., BORKAR V.S., MITTER S.K., "A unified framework for hybrid control: Model and optimal control theory". IEEE Transactions on Automatic Control, 43, 1, p. 31-45, 1998.

....is left to schemes based on heuristic rules inferred by practical plant operation. Recently, in the literature researchers started dealing with hybrid systems, namely hierarchical systems constituted by dynamical components at the lower level, governed by upper level logical discrete components [22, 2]. For this class of systems, design procedures have been proposed which naturally lead to hierarchical, hybrid control schemes, with continuous controllers at the lower level calibrated for each dynamical subsystem in order to provide regulation and tracking properties, and discrete controllers ....

.... # 1 (t) Hence, by (5a) # 2 (t) # (1 # 1 (t) 42a) # 2 (t) # (1 x # (t) 42b) # 2 (t) # (1 # 1 (t) 1 x # (t) 1 (42c) The mixed integer linear inequalities (41) 42) define the automaton part in system (39) which hence is a MLD system. As a further example, a recent paper [2] describes how to associate a finite automaton similar to the one depicted in Fig. 3 with hysteresis functions. Therefore, physical systems a#ected by hysteresis phenomena, which frequently occur in di#erent contexts (e.g. magnetic, electrical, etc. can be easily modeled in the MLD form (9) ....

M.S. Branicky, V.S. Borkar, and S.K. Mitter. A unified framework for hybrid control: model and optimal control theory. IEEE Trans. Autom. Contr., 43(1):31--45, 1998.

.... a special class of hybrid systems by merging the notion of control systems 1 The notations q(t ) and q(t ) refer to the limiting processes lim s#t q(s) and lim s#t q(s) on manifolds with an a#ne connection, see [12] and that of controlled general hybrid dynamical system, see [2]. The fundamental discrete phenomena we model are controlled switches between distinct sets of constraints, resulting in impacts. The underlying structure is a mechanical control system (Q, M q , F) together with a given set of constraint distributions D i , where i belongs to an index set I . ....

....of controls. At any point, we can choose to jump to any other discrete state through impact and in general we also have several di#erent impacts to choose from (indexed by the set of discrete inputs V ij ) 2. 5 Remarks There are a number of di#erences between our definition and the definition in [2]. The controlled jump sets are in our case equal to Q and are thus omitted. Furthermore, we impose more structure on the controlled jump destination maps: at each point q # Q we can choose to change the discrete state from i to j by undergoing an impact. During the impact, the velocity is mapped ....

[Article contains additional citation context not shown here]

M. S. Branicky, V. S. Borkar, and S. K. Mitter. A unified framework for hybrid control: model and optimal-control theory. IEEE TAC, 43(1):31--45, 1998.

....the problem is decidable. 1 Introduction The design of controllers is one of the most active research topics in the area of hybrid systems. Problems that have been addressed include hierarchical control [20, 5] distributed control [18] and optimal control using dynamic programming techniques [4, 3, 25, 21] or extensions of the maximum principle [12] A substantial research effort has also been directed towards solving control problems with reachability specifications, that is designing controllers that guarantee that the state of the system remains in a good part of the state space. Such control ....

Michael S. Branicky, Vivek S. Borkar, and Sanjoy K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Transactions on Automatic Control, 43(1):31--45, 1998.

....automata theory totim d autom ,wherethe continuous time flow is modeled as x = 1, and further to linear hybrid autom: 1] where the dynamic is specifiedb y the di#erential inclusion a # x # b. On the other side, the control community started studyingthe so called hybrid dynam: al system [11] or hybridautom:1 [26] where the switchingb etween di#erent dynamics is governedb y a finite automaton. A special case where dynamic equations and switchingrules are linear functions of the state are the so called Piece Wise A#ne (PWA) systems [33] Recently, Bemporad and Morari [4] introduced a ....

....system of Section II A. It is easy to check from (6a) 9) that only the combgB( Djg [# 1 ,# 2 ,# 3 ,# 4 ] reported in Tab# 2 are allowed. The correspondin relationsb etween z and x, u are also reported in Tab( 2. # 1 #2 #3 #4] z = G(x, u) 0 0 00] 0 1 10] z = 00] x [0] u 0 [1 0 00] [0 0 11] [0 1 11] z = 00] x [1] u 0 [1 0 01] TABLE I I Vali combi ti [# 1 #2 #3 #4] andrespecti functiti z = G(x, u) As the switchingis governedb y changes of vector #(t) it is intuitive that the numb er of regions in which the state space R 2 is partitioned coincides with the numb er of ....

[Article contains additional citation context not shown here]

M.S. Branicky, V.S. Borkar, and S.K. Mitter.A unified framework for hybrid control: model and optimal control theory. IEEE Trans. Automatic Control, 43(1):31--45, 1998.

....on heuristic rules inferred by practical plant operation. Recently, in the literature researchers started dealing with hybrid systems, namely hierarchical systems constituted by dynamical components at the lower level, governed by upper level logical discrete components (Grossmann et al. 1993; Branicky et al. 1998). Hybrid systems arise in a large number of application areas, and are attracting increasing attention in both academic theory oriented circles as well as in industry. Our interest is motivated by several clearly discernible trends in the process industries which point toward an extended need for ....

....# # (t)4(1 # # (t) 42a) # # (t)4(1 x l (t) 42b) # # (t)5(1 # # (t) #(1 x l (t) 1. 42c) The mixed integer linear inequalities (41) 42) along with the equality x l (t#1) # # (t) define the automaton part in system (39) which hence is a MLD system. As a further example, Branicky et al. 1998) describe how to associate a finite automaton similar to the one depicted in Fig. 2 with hysteresis phenomena which frequently occur in different contexts (e.g. magnetic, electrical, etc. Finally, time dependence can be emulated in the time invariant MLD Fig. 2. Automaton driven by conditions on ....

Branicky, M. S., Borkar, V. S., & Mitter, S. K. (1998). A unified framework for hybrid control: model and optimal control theory.

....the problem is decidable. 1 Introduction The design of controllers is one of the most active research topics in the area of hybrid systems. Problems that have been addressed include hierarchical control [5, 19] distributed control [18] and optimal control using dynamic programming techniques [3, 4, 20, 23] or extensions of the maximum principle [11] A substantial research effort has also been directed towards solving control problems with reachability specifications, that is designing controllers that guarantee that the state of the system will remain in a good part of the state space. Such ....

M.S. Branicky, V.S. Borkar, and S.K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Transactions on Automatic Control, 43(1):31--45, 1998.

No context found.

M.S. Branicky, V.S. Borkar, and S.K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Trans. Automatic Control, 43(1):31--45, 1998.

....immediately. Examples of these jumps include a ball bouncing (with modeled instantaneous reset of velocity) and gear switching (with a choice of when to change dynamics and which to change to) 1. 2 Hybrid Bellman Equation Controls for the above may be computed using an optimal control framework [4]. Roughly, this is done by adding running costs to the contin uous state and controls, k(x,q,u) autonomous jump costs, ca(x,q,v) and controlled jump costs, co(s, s) where s, s are the hybrid source and des tination states. In [4] existence of solutions to the optimal control problem (for an ....

....the above may be computed using an optimal control framework [4] Roughly, this is done by adding running costs to the contin uous state and controls, k(x,q,u) autonomous jump costs, ca(x,q,v) and controlled jump costs, co(s, s) where s, s are the hybrid source and des tination states. In [4], existence of solutions to the optimal control problem (for an even more general) is proven, under various technical assumptions. A set of Gen eralized Quasi Variational Inequalities (GQVIs) is derived that characterize the optimal value function. Briefly, these equations generalize both the ....

M.S. Branicky, V.S. Borkar, and S.K. Mit- ter, A unified framework for hybrid control: Model and optimal control theory, IEEE Trans. Auto- matic Control, 43(1):31-45, 1998.

....(x(t 1 ) q 1 ) D(x(t 1 ) u, q 0 ) from which the evolution continues. While terse, the above model encompasses both autonomous and controlled switching and jumps, and allows modeling of a large class of embedded systems, including for example ground, air and space vehicles and robots; see [4, 3] for more details. Given a model of the system in the form (1.1) the path planning problem can be shortly stated as finding a (controlled) trajectory of the system that leads from a start to a goal configuration. 1 Attempts to fight the curse of dimensionality have led to the introduction of ....

M.S. Branicky, V.S. Borkar, and S.K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Trans. Automatic Control, 43(1):31--45, 1998.

.... [63] and Tavernini [64] However, in the last decade or so, hybrid system modeling has evolved dramatically beginning with Peleties and DeCarlo [50] 65] 68] and continuing with Stiver et al. 69] 70] Alur et al. 71] Nerode et al. 72] 73] Dogruel Ozguner [74] Branicky [51] [75], 76] and, more recently, Pettersson et al. 49] 77] 78] A review of these models is beyond the scope of this paper. Nevertheless, the pertinent fruit of the modeling evolution can be summarized by the dynamics (2.1a) 2.1b) 2.1c) where is the continuous time state, can be either a ....

M. S. Branicky, V. S. Borkar, and S. K. Mitter, "A unified framework for hybrid control: Model and optimal control theory," IEEE Trans. Automat. Contr., vol. 43, no. 1, pp. 31--45, 1998.

.... are discrete or higher level switching dynamics (which can be captured as an automaton or graph structure) combined with the lower level dynamics (usually continuous state and given by differential or difference equations) An optimal control theory for suchsystems has been developed (see, e.g. [3, 5, 4]) Unfortunately,such solutions are based on dynamic programming and inevitably suffer from a curse of dimensionality. Lately,wehave been intrigued with the possibility of speeding up the solution to such problems by considering techniques that takeadvantage of the underlying properties of the ....

M.S. Branicky, V.S. Borkar, and S.K. Mitter, A unified framework for hybrid control: Model and optimal control theory, IEEE Trans. Automatic Control, 43(1):31--45, 1998.

No context found.

Branicky, M. S., Borkar, V. S., and Mitter, S. K. (1998). A unified framework for hybrid control: Model and optimal theory. IEEE Trans. Automatic Control 43 (1), 31--45.

No context found.

M. Branicky, V. Borkar, and S. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Transactions on Automatic Control, 43(1):31--45, 1998.

No context found.

M. S. Branicky, V. S. Borkar, and S. K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Transactions on Automatic Control, 43:31=45, 1998.

No context found.

M.S.Branicky,V.S.Borkar,andS.K.Mitter, "A unified framework for hybrid control: Model and optimal control theory," IEEE Trans. on Automatic Control, vol.4 3, no. 1 , pp. 31---4 5, 1998.

No context found.

M. S. Branicky, V. S. Borkar, and S. K. Mitter. A unified framework for hybrid control: Model and optimal control theory. IEEE Transactions on Automatic Control, 43(1):31--45, 1998.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC