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62
Model Predictive Control of Coordinated MultiVehicle Formations
 In IEEE Conference on Decision and Control
, 2002
"... A generalized model predictive control (MPC) formulation is derived that extends the existing theory to a multivehicle formation stabilization problem. The vehicles are individually governed by nonlinear and constrained dynamics. The extension considers formation stabilization to a set of permis ..."
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Cited by 68 (10 self)
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A generalized model predictive control (MPC) formulation is derived that extends the existing theory to a multivehicle formation stabilization problem. The vehicles are individually governed by nonlinear and constrained dynamics. The extension considers formation stabilization to a set of permissible equilibria, rather than a unique equilibrium. Simulations for three vehicle formations with input constrained dynamics on configuration space SE(2) are performed using a nonlinear trajectory generation (NTG) software package developed at Caltech. Preliminary results and an outline of future work for scaling/decentralizing the MPC approach and applying it to an emerging experimental testbed are given.
Unconstrained Receding Horizon Control with No Terminal Cost
, 2001
"... In this paper, we discuss a stabilizing receding horizon scheme for unconstrained nonlinear systems. Using Dini's theorem on the uniform convergence of functions, we show that there always exist a finite horizon length for which the corresponding receding horizon scheme is stabilizing without u ..."
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Cited by 55 (11 self)
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In this paper, we discuss a stabilizing receding horizon scheme for unconstrained nonlinear systems. Using Dini's theorem on the uniform convergence of functions, we show that there always exist a finite horizon length for which the corresponding receding horizon scheme is stabilizing without using terminal costs and/or constraints.
Cooperative hybrid control of robotic sensors for perimeter detection and tracking
 in Proc. American Control Conf
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Nonlinear Receding Horizon Control of F16 Aircraft
 Journal of Guidance, Control, and Dynamics
, 2002
"... In this paper the application of receding horizon control (RHC) with the linear parameter varying (LPV) design methodology to a high delity, nonlinear F16 aircraft model is demonstrated. The highlights of the paper are i)Use of RHC to improve upon the performance of a LPV regulator. ii)Discussion ..."
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Cited by 28 (8 self)
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In this paper the application of receding horizon control (RHC) with the linear parameter varying (LPV) design methodology to a high delity, nonlinear F16 aircraft model is demonstrated. The highlights of the paper are i)Use of RHC to improve upon the performance of a LPV regulator. ii)Discussion on details of implementation such as control space formulation, tuning of RHC parameters, computation time and numerical properties of the algorithms. iii)Simulated response of nonlinear RHC and LPV regulator.
Nonlinear Optimal Control: A Control Lyapunov Function and Receding Horizon Perspective
 Asian Journal of Control
, 1999
"... Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). The online EulerLagrange computation of receding horizon control is naturally viewed in terms of optimal control, whe ..."
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Cited by 27 (0 self)
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Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). The online EulerLagrange computation of receding horizon control is naturally viewed in terms of optimal control, whereas researchers in CLF methods have emphasized such notions as inverse optimality. We focus on a CLF variation of Sontag's formula, which also results from a special choice of parameters in the socalled pointwise minnorm formulation. Viewed this way, CLF methods have direct connections with the HamiltonJacobiBellman formulation of optimal control. A single example is used to illustrate the various limitations of each approach. Finally, we contrast the CLF and receding horizon points of view, arguing that their strengths are complementary and suggestive of new ideas and opportunities for control design. The presentation is tutorial, emphasizing concepts and connections over details and t...
Decentralized robust receding horizon control for multivehicle guidance
"... Abstract — This paper presents a decentralized robust Model Predictive Control algorithm for multivehicle trajectory optimization. The algorithm is an extension of a previous robust safe but knowledgeable (RSBK) algorithm that uses the constraint tightening technique to achieve robustness, an invar ..."
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Cited by 25 (8 self)
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Abstract — This paper presents a decentralized robust Model Predictive Control algorithm for multivehicle trajectory optimization. The algorithm is an extension of a previous robust safe but knowledgeable (RSBK) algorithm that uses the constraint tightening technique to achieve robustness, an invariant set to ensure safety, and a costtogo function to generate an intelligent trajectory around obstacles in the environment. Although the RSBK algorithm was shown to solve faster than the previous robust MPC algorithms, the approach was based on a centralized calculation that is impractical for a large group of vehicles. This paper decentralizes the algorithm by ensuring that each vehicle always has a feasible solution under the action of disturbances. The key advantage of this algorithm is that it only requires local knowledge of the environment and the other vehicles while guaranteeing robust feasibility of the entire fleet. The new approach also facilitates a significantly more general implementation architecture for the decentralized trajectory optimization, which further decreases the delay due to computation time.
Receding Horizon Control of The Caltech Ducted Fan: A Control Lyapunov Function Approach.
, 1999
"... This paper deals with the application of receding horizon methods to the simplified model of a flight control experiment developed at Cal Tech. The dynamics of the system are representative of a Vertical Landing and Take off (VTOL) aircraft, such as a Harrier around hover. The adopted control method ..."
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Cited by 18 (9 self)
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This paper deals with the application of receding horizon methods to the simplified model of a flight control experiment developed at Cal Tech. The dynamics of the system are representative of a Vertical Landing and Take off (VTOL) aircraft, such as a Harrier around hover. The adopted control methodology is a hybrid of receding horizon techniques and Control Lyapunov Function (CLF) based ideas. First a CLF is found, and then, by using the CLF as the terminal cost in the receding horizon optimization, stability is guaranteed. It is shown that if the horizon length is long enough, a simple choice of CLF, i.e., the one obtained from Jacobian linearization of the dynamics at hover, will achieve a good performance. However, if due to computational costs, longer time horizons are not possible, stability can be guaranteed by applying the CLF obtained using QuasiLPV methods, as a terminal costs. Several numerical simulations for different time horizons are presented to illustrate the effectiveness of the discussed methods.
Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics
"... Abstract—This paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models— systems with impulse effects—through control Lyapunov functions. The periodic orbit is assumed to lie in a C 1 submanifold Z that is contained in the zero set of an output func ..."
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Cited by 13 (10 self)
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Abstract—This paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models— systems with impulse effects—through control Lyapunov functions. The periodic orbit is assumed to lie in a C 1 submanifold Z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics; the associated restriction dynamics are termed the hybrid zero dynamics. The orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics. Prior results on the stabilization of such periodic orbits with respect to the fullorder dynamics of the system with impulse effects have relied on inputoutput linearization of the dynamics transverse to the zero dynamics manifold. The principal result of this paper demonstrates that a variant of control Lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface, Z, can be used to achieve exponential stability of the periodic orbit in the fullorder dynamics, thereby significantly extending the class of stabilizing controllers. The main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control Lyapunov functions. I.
On Output Feedback Nonlinear Model Predictive Control Using High Gain Observers For A Class Of Systems
, 2001
"... In recent years, nonlinear model predictive control schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in connection to nonlinear predictive control. Mo ..."
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Cited by 12 (4 self)
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In recent years, nonlinear model predictive control schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in connection to nonlinear predictive control. Most of the existing approaches for output feedback nonlinear model predictive control do only guarantee local stability. Here we consider the combination of stabilizing instantaneous NMPC schemes with high gain observers. For a special MIMO system class we show that the closed loop is asymptotically stable, and that the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme are recovered for a high gain observer with large enough gain and thus leading to semiglobal/nonlocal results.
Optimal control of a double inverted pendulum on a cart
 CSEE, OGI School of Science and Engineering, OHSU
, 2004
"... In this report a number of algorithms for optimal control of a double inverted pendulum on a cart (DIPC) are investigated and compared. Modeling is based on EulerLagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. This results i ..."
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Cited by 10 (0 self)
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In this report a number of algorithms for optimal control of a double inverted pendulum on a cart (DIPC) are investigated and compared. Modeling is based on EulerLagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. This results in a system of nonlinear differential equations consisting of three 2nd order equations. This system of equations is then transformed into a usual form of six 1st order ordinary differential equations (ODE) for control design purposes. Control of a DIPC poses a certain challenge, since unlike a robot, the system is underactuated: one controlling force per three degrees of freedom (DOF). In this report, problem of optimal control minimizing a quadratic cost functional is addressed. Several approaches are tested: linear quadratic regulator (LQR), statedependent Riccati equation (SDRE), optimal neural network (NN) control, and combinations of the NN with the LQR and the SDRE. Simulations reveal superior performance of the SDRE over the LQR and improvements provided by the NN, which compensates for model inadequacies in the LQR. Limited capabilities of the NN to approximate functions over the wide range of arguments prevent it from significantly improving the SDRE performance, providing only marginal benefits at larger pendulum deflections. 1