C. J. Tomlin, Hybrid Control of Air Traffic Management Systems. PhD thesis, Department of Electrical Engineering, University of California, Berkeley, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to achieve scalable designs. Among heterogeneous modeling techniques, the integration of continuous and discrete dynamics has received attention in system theory [3] 18] micro electromechanical devices and systems (MEMS) 29] computer aided design (CAD) 2] 5] 30] and automatic control [7][31], among other communities. Two kinds of integration have been widely accepted by modeling and design theories and practices the mixed signal style that integrates continuous time differential equations with timebased discrete event models and the hybrid system style that integrates differential ....

C. Tomlin, Hybrid Control of Air Traffic Management Systems, Ph.D. thesis, Department of EECS, University of California, Berkeley, CA 94720, 1998.

....is the study of hybrid systems [2] Solid theoretical frameworks for modeling and analyzing hybrid systems are under rapid development [ 1, 4, 7, 10, 14] with applications in air traffic control, transportation systems, automotive, manufacturing systems, and electromechanical systems etc. [3, 16, 17]. Nevertheless, a simulation tool with clean semantics and composability that leverages the theory of hybrid system is still under high demand [15] Communication Contents . This work is part of the Ptolemy project, which is supported by DARPA ITO, the State of California MICRO program, and ....

Claire Tomlin, Hybrid Control of Air Traffic Management Systems, Ph.D. Thesis, Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, 1998.

....the origin (left subplot is a recreation of figure 7 from [1] right barrier (between circle and star) L2.1 lies between circle and triangle, L2.2 between triangle and square, and L2.3 between square and star. 2 Adaptation to Aircraft Collision Avoidance For the two vehicle game described in [2, 3], the evader (control) lies at the origin and is surrounded by the capture circle. In the relative coordinate system dynamics (1) the input rl is attached not to the pursuer, but to the vehicle at the origin (and conversely for r2) consequently, to compute results for the aircraft game we must ....

....be made to the equations from the previous section in order to place the evader at the origin instead of the pursuer. During our analysis we swap the inputs now the evader uses input rl and the pursuer r2 but do not make the other changes necessary to convert fully to the example presented in [2] (except for figure 7 at the end of section 2.5; we explain the other necessary changes in the figure s accompanying text) 15 2.1 Optimal Trajectories The same terminal conditions apply, but now the coordinate system is relative to the evader at the origin. Therefore, 3) changes to ix(0) ....

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C. J. Tomlin, Hybrid Control of Air Traffic Management Systems. Ph.D. thesis, Depart- ment of Electrical Engineering, University of California, Berkeley, 1998.

....dynamics is the study of hybrid systems [2] Solid theoretical frameworks for modeling and analyzing hybrid systems are under rapid development [1, 4, 7, 10, 14] with applications in air traffic control, transportation systems, automotive, manufacturing systems, and electromechanical systems etc. [3, 16, 17]. Nevertheless, a simulation tool with clean semantics and composability that leverages the theory of hybrid system is still under high demand [15] This work is part of the Ptolemy project, which is supported by DARPA ITO, the State of California MICRO program, and the following companies: ....

Claire Tomlin, Hybrid Control of Air Traffic Management Systems, Ph.D. Thesis, Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, 1998.

....and dynamics are modeled by points in R n and differential equations, respectively. Symbolic model checking on a hybrid automaton provides correctness guarantees. HyTech [10] is a model checker for hybrid systems that has been successful in analyzing many hybrid systems of practical interest [2, 5, 13 16, 23, 26, 27]. Despite its successes, HyTech has several shortcomings. It restricts the dynamical model of the automaton being analyzed to that of linear hybrid automata. In linear hybrid automata, the continuous dynamics are governed by polyhedral differential inclusions, and all trajectories are composed of ....

....the loss of precision caused by the accumulation of round off errors in the numerical integration process may lead the analyzer, whether human or computer, to overlook potentially hazardous events. In contrast to hybrid systems simulators (see [21] for a survey) and reachset computation tools [3, 4, 6, 8, 26] which use traditional (not interval based) numerical methods, HyperTech is guaranteed not to miss any events. Thus, if an unsafe (target) state of a hybrid automaton is reachable, HyperTech is guaranteed to note its reachability. 3 The rest of the paper is organized as follows. In Section 2, we ....

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C.J. Tomlin. Hybrid Control of Air Traffic Management Systems. PhD thesis, University of California at Berkeley, 1998.

....is the study of hybrid systems [2] A solid theoretical framework for modeling and analyzing hybrid systems is under rapid development [1, 4, 8, 10, 15] with applications in air traffic management, transportation systems, automotive, manufacturing systems, and electromechanical systems etc. [3, 6, 20, 21]. Nevertheless, a simulation tool with clean semantics and composability that leverages the theory of hybrid system is still under high demand [16] Component based models view the building blocks of a system to be components. As shown in Figure 1, components are black boxes. The interface of a ....

....Client Server Programming with JAVA and CORBA, Wiley Computer Publishing, 1997. 18] R. A. Saleh and A. R. Newton, Mixed Mode Simulation, Kluwer Academic Publishers, 1990. 19] D.A. Schmidt, Denotational Semantics: A Methodology for Language Development, Allyn and Bacon, Newton, MA, 1986. [20] Claire Tomlin, Hybrid Control of Air Traffic Management Systems, Ph.D. Thesis, Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, 1998. 21] P. Varaiya, Smart cars on smart roads: problems of control, IEEE Trans. on Automatic Control, vol.38, ....

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Claire Tomlin, Hybrid Control of Air Traffic Management Systems, Ph.D. Thesis, Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, 1998.

.... case of timed games (which corresponds to timed automata) 6, 16, 20] and for rectangular games under the assumption that the controller can move only at integer points in time (sampling control) 13] Semialgorithms for control have also been proposed for more general linear [27] and nonlinear [18, 26] hybrid games, but in these cases termination is not guaranteed. The algorithms for timed games and sampling control are based on the fact that the underlying state spaces can be partitioned into finitely many bisimilarity classes, and the controller does not need to distinguish between bisimilar ....

Tomlin, C.: Hybrid Control of Air Traffic Management Systems. Ph.D. thesis, University of California, Berkeley (1998)

.... verification of this kind of hybrid systems can be extremely hard, and is often foregone in favor of simulations [15] Other hybrid system architectures proposed for air traffic conflict resolution have a rigorous mathematical foundation, but do not provide feasible trajectories for the system [11, 16], and as such cannot be applied for motion planning at scales at which the dynamics of the vehicle are important. In a second class of applications the main objective of the hybrid control architecture is ensuring the correct execution of maneuvers involving transitions between different operating ....

C. Tomlin. Hybrid Control of Air Traffic Management Systems. PhD thesis, University of California at Berkeley, 1998.

....in practice, and approximation methods must be used. Some approximation methods bound the dynamics by piecewise constant inclusions, e.g. rate translation (Henzinger, Ho, Wong Toi 1998) others use numerical integration (Chutinan Krogh 1998; Dang Maler 1998; Greenstreet Mitchell 1998; Tomlin 1998). Unfortunately, traditional numerical integration methods suffer from roundoff errors, and do not necessarily yield validated results. On the other hand, accurate rate translation suffers from state ex plosion. In contrast to traditional numerical methods, interval numerical methods yield ....

Tomlin, C. 1998. Hybrid Control of Air Traffic Management Systems. Ph.D. Dissertation, University of California at Berkeley.

....of deflecting flaps is assumed to be minor. Thus, we choose to model the flap setting as a discrete variable. The results in this section are taken from [48] A simple point mass model for aircraft vertical navigation is used, which accounts for lift L, drag D, thrust T, and gravity mg (see [73] and references therein) We model the nonlinear longitudinal dynamics D(a, V) Tcosa mg sin L(a, V) T sina mg cos V sin y (12) in which the state x = V, z] 6 R s includes the aircraft s speed V, flightpath angle , and altitude z. We assume the control input u = T, a] with ....

C. J. Tomlin, Hybrid Control of Air Traffic Management Systems. PhD thesis, Department of Electrical Engineering, University of California, Berkeley, 1998.

....time , evolves according to (2) with input , and ends at the final state , with cost . This choice of value function, which only depends on the final state, encodes the binary state of safe or not safe, at the final state. Using standard techniques in optimal control theory [27] and dynamic games [23], 28] one can show that the optimal control and worst disturbance are given by: 8) 9) where is the vector field given by the right hand side of (2) and represents the gradient of . The optimal value function evolves according to the Hamilton Jacobi equation: 10) where . To ensure that ....

C. J. Tomlin, "Hybrid Control of Air Traffic Management Systems," Ph.D. dissertation, Dep. Elect. Eng., Univ.of California, Berkeley, CA, 1998.

....be simplified by representing a set of behaviors as a single discrete state or mode with simplified continuous dynamics. As such, a hybrid system is a continuous state system with switches [21] in which the switches have a defining logic which may be modeled by a discrete transition system. In [22, 23, 24], we have developed a method for analyzing and proving the safety of hybrid systems. We translate safety specifications into restrictions on the system s reachable sets of states. Then, using analysis based on two person zero sum game theory for automata and continuous dynamical systems, we derive ....

....and ends at the final state x(0) with cost x r (0) 2 y r (0) 2 Gamma 5 2 . This choice of value function, which only depends on the final state, encodes the binary state of safe or not safe, at the final state. Using standard techniques in optimal control theory [27] and dynamic games [28, 23], one can show that the optimal control u and worst disturbance d are given by: u (x) max u2U min d2D r J(x; u; d; t) T f(x; u; d) 8) d (x) min d2D r J(x; u ; d; t) T f(x; u ; d) 9) where f(x; u; d) is the vector field given by the right hand side of (2) and r J ....

C. J. Tomlin, Hybrid Control of Air Traffic Management Systems. PhD thesis, Department of Electrical Engineering, University of California, Berkeley, 1998.

....within this safe region. This controller must be overridden whenever the system reaches the boundary of the safe space. In this paper, we address the design of the performance controller under the restrictions of the safety controller. Our methodology combines the Hamilton Jacobi approach of [3] (for systems in which we can find closed form representations of the safe space) and nonlinear optimization techniques [4, 5] by viewing the restrictions necessary for safety as inequality constraints in a nonlinear optimization problem. A similar problem of incorporating state and control ....

....Description We address the problem of combining safety and performance goals for a hybrid system in a single discrete mode, that is, for the nonlinear continuous dynamics: x = f(x; u) 1) with state x 2 X , and control input u 2 U . Given an initial unsafe region G ae X , we follow the method of [3] to compute the maximal controlled invariant set contained in G c , which is denoted W ae X . W represents those states from which there exists a control input u 2 U such that the system can remain in W for all future time. We also compute the set valued feedback control law U safe (x) which ....

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C. Tomlin, Hybrid Control of Air Traffic Management Systems. PhD thesis, University of California, Berkeley, CA, September 1998.

....constant rate dynamics. Tools have been developed to perform such calculations automatically [3, 4] and to synthesize controllers in such a framework [5, 6] Control theorists have extended reachability tools from continuous state and time dynamical systems theory to incorporate discrete switches [7 11]. However, the efficient computation of reachable sets for hybrid systems with nonlinear dynamics remains a difficult problem to solve. Numerical techniques which over approximate the nonlinear dynamics with linear dynamics [12] or which over approximate the reachable sets [13 16] have recently ....

....Program (AFRL contract F33615 99 C 3014) and by a Frederick E. Terman Faculty Award. In this paper, we present an implementation of an exact reachability operator for nonlinear hybrid systems. An algorithm which synthesizes control laws for such systems based on the Hamilton Jacobi equation [9 11] is reviewed, and then a new Hamilton Jacobi formulation with superior numerical properties is developed and proved to be equivalent. While level set techniques were previously investigated for the solution of such equations in [17] we have added several improvements to the basic level set ....

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C. J. Tomlin, Hybrid Control of Air Traffic Management Systems. PhD thesis, Department of Electrical Engineering, University of California, Berkeley, 1998.

...., there exists a d( 2 D such that x(t) x, x(0) 2 G, and x( for t 0 is the solution to (1) This problem may be solved using the framework of differential game theory [5, 6] by constructing a value function J(x; u; d; t) such that J(x; u; d; 0) has zero level set on the boundary of G. In [7], the boundary of the reachable set V is shown to be the zero level set of the solution J (x; t) to the following Hamilton Jacobi equation: Gamma J (x; t) t = 8 : J (x;t) x f(x; u ; d ) for fx 2 X : J (x; t) 0g minf0; J (x;t) x f(x; u ; d )g ....

.... u( Delta) d( Delta) t) 8) and corresponding optimal input and disturbance as u ( Delta) arg max u( Delta)2U min d( Delta)2D J(x; u( Delta) d( Delta) t) 9) d ( Delta) arg min d( Delta)2D J(x; u ( Delta) d( Delta) t) 10) Applying the development in [5] Chapter 4) and [7] (Chapter 4) to the linear differential game (4) we have H = p T (Ax Bu Cd) 11) p T = Gamma H x = Gammap T A (12) p T (0) T = Q g x(0) Gamma q g ) T Q g (13) u ( Delta) arg max u2U min d2D H(x; p; u; d) 14) d ( Delta) arg min d2D H(x; p; u ; d) ....

Claire J. Tomlin. Hybrid Control of Air Traffic Management Systems. PhD thesis, Department of Electrical Engineering, University of California, Berkeley, 1998.

....[6] and [5] the authors have designed switched control laws based on the linearized dynamics of the aircraft. The authors in [7] have designed a continuous nonlinear control law for the lateral axis dynamics of the Harrier. Our work builds on previous work in controlling nonlinear hybrid systems [8, 9, 10], in which a least restrictive control law for the nonlinear longitudinal dynamics of a conventional aircraft was developed. In this paper, we develop a nonlinear dynamic model of the longitudinal axis dynamics of a Harrier aircraft. We abstract the longitudinal behavior into three modes of ....

....constraints on ffi 2 [ffi min ; ffi max ] and ffi 2 [ ffi min ; ffi max ] These limits describing the boundary of the envelope are functions of such factors as airspace regulations, type of aircraft, and weather, yet we assume for simplicity that all limits are constants within each mode. [9, 10] presents an algorithm for computing the least restrictive control law for such systems, which carves out the maximal controlled invariant subset of the aerodynamic flight envelope. We define a value function J(x; u; t) n Theta u Theta Gamma1 such that J(x; u ; 0) l(x) ....

C. Tomlin. Hybrid Control of Air Traffic Management Systems. PhD thesis, University of California, Berkeley, CA, September 1998.

....and collision avoidance algorithms have been developed to provide directives to the evading aircraft. These works used empirical and Monte Carlo simulation techniques to obtain the results. An alternative method using analysis based on differential game theory was proposed by previous researchers [5,6] for aircraft collision avoidance problems. Our paper applies this approach specifically to the closely spaced parallel approach (CSPA) problem. The first section of the paper describes how the CSPA is posed as a differential game problem. It also provides the analysis and explains the results ....

Tomlin, C. J., 1998, Hybrid Control of Air Traffic Management Systems, Phd. Thesis, Univ. of California, Berkeley.

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Tomlin, C. J., Hybrid Control of Air Traffic Management Systems, Ph.D. thesis, Department of Electrical Engineering, University of California, Berkeley, 1998.

....solution concept for the PDEs. A brief comparison with other techniques proposed in the literature for computing or approximating the reach set of hybrid systems is also given. We demonstrate the application of this approach to a new example from aircraft collision avoidance, developed from [9] (Section 5) 2 Model For a finite collection V of variables, let V denote the set of valuations of these variables, i.e. the set of all possible assignments of the variables in V . For example, if x is a state variable taking values in R n we write X = fxg with X = R n . By abuse of ....

Claire J. Tomlin, Hybrid Control of Air Traffic Management Systems, PhD thesis, Department of Electrical Engineering, University of California, Berkeley, 1998.

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