Results 1  10
of
36
Switching mode generation and optimal estimation with application to skidsteering
 Automatica
"... Skidsteered vehicles, by design, must skid in order to maneuver. The skidding causes the vehicle to behave discontinuously during a maneuver as well as introduces complications to the observation of the vehicle’s state, both of which affect a controller’s performance. This paper addresses estimatio ..."
Abstract

Cited by 15 (13 self)
 Add to MetaCart
(Show Context)
Skidsteered vehicles, by design, must skid in order to maneuver. The skidding causes the vehicle to behave discontinuously during a maneuver as well as introduces complications to the observation of the vehicle’s state, both of which affect a controller’s performance. This paper addresses estimation of contact state by applying switched system optimization to estimate skidding properties of the skidsteered vehicle. In order to treat the skidsteered vehicle as a switched system, the vehicle’s ground interaction is modeled using Coulomb friction, thereby partitioning the system dynamics into four distinct modes, one for each combination of the forward and back wheel pairs sticking or skidding. Thus, as the vehicle maneuvers, the system propagates over some mode sequence, transitioning between modes over some set of switching times. This paper presents secondorder optimization algorithms for estimating these switching times. We emphasize the importance of the secondorder algorithm because it exhibits quadratic convergence and because even for relatively simple examples, firstorder methods fail to converge on time scales compatible with realtime operation. Furthermore, the paper presents a technique for estimating the mode sequence by optimizing a relaxation of the switched system.
A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems: Appendix.
, 2010
"... ABSTRACT One of the oldest problems in the study of dynamical systems is the calculation of an optimal control. Though the determination of a numerical solution for the general nonconvex optimal control problem for hybrid systems has been pursued relentlessly to date, it has proven difficult, since ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
(Show Context)
ABSTRACT One of the oldest problems in the study of dynamical systems is the calculation of an optimal control. Though the determination of a numerical solution for the general nonconvex optimal control problem for hybrid systems has been pursued relentlessly to date, it has proven difficult, since it demands nominal mode scheduling. In this paper, we calculate a numerical solution to the optimal control problem for a constrained switched nonlinear dynamical system with a running and final cost. The control parameter has a discrete component, the sequence of modes, and two continuous components, the duration of each mode and the continuous input while in each mode. To overcome the complexity posed by the discrete optimization problem, we propose a bilevel hierarchical optimization algorithm: at the higher level, the algorithm updates the mode sequence by using a singlemode variation technique, and at the lower level, the algorithm considers a fixed mode sequence and minimizes the cost functional over the continuous components. Numerical examples detail the potential of our proposed methodology.
Optimal control of switching times in hybrid systems
 MMAR'2003, Miedzyzdroje
, 2003
"... Abstract. This paper considers the problem of determining optimal switching times at which mode transitions should occur in multimodal, hybrid systems. An expression for the gradient of the cost functional, defined with respect to the switching times, is presented in such a way that not only the sw ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
(Show Context)
Abstract. This paper considers the problem of determining optimal switching times at which mode transitions should occur in multimodal, hybrid systems. An expression for the gradient of the cost functional, defined with respect to the switching times, is presented in such a way that not only the switching times, but also the number of switches can be incorporated in the problem formulation. Numerical examples testify to the viability of the proposed approach. Key Words. Switched dynamical systems, switchingtime control, optimal control, hybrid systems, gradientdescent algorithms. 1.
Optimal control of switching surfaces
 in 43rd IEEE Conference on Decision and Control
, 2004
"... Abstract — This paper studies the problem of optimal switching surface design for hybrid systems. In particular, a formula is derived for computing the gradient of a given integral performance cost with respect to the switching surface parameters. The formula reflects the hybrid nature of the system ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
Abstract — This paper studies the problem of optimal switching surface design for hybrid systems. In particular, a formula is derived for computing the gradient of a given integral performance cost with respect to the switching surface parameters. The formula reflects the hybrid nature of the system in that it is based on a costate variable having a discrete element and a continuous element. A numerical example with a gradient descent algorithm suggests the potential viability of the formula in optimization.
Efficient suboptimal solutions of switched LQR problems
 IN PROCEEDINGS OF THE AMERICAN CONTROL CONFERENCE, ST
, 2009
"... This paper studies the discretetime switched LQR (DSLQR) problem using a dynamic programming approach. Based on some nice properties of the value functions, efficient algorithms are proposed to solve the finitehorizon and infinitehorizon suboptimal DSLQR problems. More importantly, we establish ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
(Show Context)
This paper studies the discretetime switched LQR (DSLQR) problem using a dynamic programming approach. Based on some nice properties of the value functions, efficient algorithms are proposed to solve the finitehorizon and infinitehorizon suboptimal DSLQR problems. More importantly, we establish analytical conditions under which the strategies generated by the algorithms are stabilizing and suboptimal. These conditions are derived explicitly in terms of subsystem matrices and are thus very easy to verify. The proposed algorithms and the analysis provide a systematical way of solving the DSLQR problem with guaranteed closeloop stability and suboptimal performance. Simulation results indicate that the proposed algorithms can efficiently solve not only specific but also randomly generated DSLQR problems, making NPhard problems numerically tractable.
On optimal quadratic regulation for discretetime switched linear systems
 IN HYBRID SYSTEMS: COMPUTATION AND CONTROL, SER. LECTURE NOTES IN COMPUTER SCIENCE, M. EGERSTEDT AND
"... This paper studies the discretetime linear quadratic regulation problem for switched linear systems (DLQRS) based on dynamic programming approach. The unique contribution of this paper is the analytical characterizations of both the value function and the optimal control strategies for the DLQRS p ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
(Show Context)
This paper studies the discretetime linear quadratic regulation problem for switched linear systems (DLQRS) based on dynamic programming approach. The unique contribution of this paper is the analytical characterizations of both the value function and the optimal control strategies for the DLQRS problem. Based on the particular structures of these analytical expressions, an efficient algorithm suitable for solving an arbitrary DLQRS problem is proposed. Simulation results indicate that the proposed algorithm can solve randomly generated DLQRS problems with very low computational complexity. The theoretical analysis in this paper can significantly simplify the computation of the optimal strategy, making an NP hard problem numerically tractable.
Optimal Impulsive Control for Point Delay Systems with Refractory Period
 IFAC Workshop on TimeDelay Systems
, 2004
"... Abstract: The optimal impulsive control problem for a system with a single discrete delay is studied. In such systems the control consists only of a sequence of modulated impulses, the control variables being the impulse times and their magnitudes. It is assumed that the systems considered all have ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
Abstract: The optimal impulsive control problem for a system with a single discrete delay is studied. In such systems the control consists only of a sequence of modulated impulses, the control variables being the impulse times and their magnitudes. It is assumed that the systems considered all have a refractory period, in the sense that once an action is taken, it takes a noninfinitesimal amount of time before a subsequent action can be taken. Necessary conditions for a stationary solution are derived and shown to extend those of the delay free case.
On the value functions of the discretetime switched lqr problem,”
 IEEE Trans. Autom. Control,
, 2009
"... AbstractIn this paper, we derive some important properties for the finitehorizon and the infinitehorizon value functions associated with the discretetime switched LQR (DSLQR) problem. It is proved that any finitehorizon value function of the DSLQR problem is the pointwise minimum of a finite n ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
AbstractIn this paper, we derive some important properties for the finitehorizon and the infinitehorizon value functions associated with the discretetime switched LQR (DSLQR) problem. It is proved that any finitehorizon value function of the DSLQR problem is the pointwise minimum of a finite number of quadratic functions that can be obtained recursively using the socalled switched Riccati mapping. It is also shown that under some mild conditions, the family of the finitehorizon value functions is homogeneous (of degree 2), is uniformly bounded over the unit ball, and converges exponentially fast to the infinitehorizon value function. The exponential convergence rate of the value iterations is characterized analytically in terms of the subsystem matrices.
On the value functions of the optimal quadratic regulation problem for discretetime switched linear systems
 In IEEE Conference on Decision and Control, Cancun
"... AbstractIn this paper, we study the value functions associated with the discretetime LQR problem for switched linear systems (DLQRS). Some important properties of the value functions and value iterations are derived. In particular, we will show that under some mild conditions, the family of the f ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
AbstractIn this paper, we study the value functions associated with the discretetime LQR problem for switched linear systems (DLQRS). Some important properties of the value functions and value iterations are derived. In particular, we will show that under some mild conditions, the family of the finitehorizon value functions of the DLQRS problem is homogeneous (of degree 2), uniformly bounded over the unit ball, and converges exponentially fast to the corresponding infinitehorizon value function. More importantly, the exponential convergence rate of the value iteration is characterized analytically in terms of the subsystem matrices. The properties derived in this paper are not only of theoretical importance, but also crucial in the analysis and design of various optimal and suboptimal control strategies for DLQRS problems.
Optimal motion planning for a class of hybrid dynamical systems with impacts
 in IEEE ICRA
, 2011
"... Abstract—Hybrid dynamical systems with impacts typically have controls that can influence the time of the impact as well as the result of the impact. The leg angle of a hopping robot is an example of an impact control because it can influence when the impact occurs and the direction of the impulse. ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract—Hybrid dynamical systems with impacts typically have controls that can influence the time of the impact as well as the result of the impact. The leg angle of a hopping robot is an example of an impact control because it can influence when the impact occurs and the direction of the impulse. This paper provides a method for computing an explicit expression for the first derivative of a cost function encoding a desired trajectory. The first derivative can be used with standard optimization algorithms to find the optimal impact controls for motion planning of hybrid dynamical systems with impacts. The resulting derivation is implemented for a simplified model of a dynamic climbing robot. I.