13,027 research outputs found
Linearly Solvable Stochastic Control Lyapunov Functions
This paper presents a new method for synthesizing stochastic control Lyapunov
functions for a class of nonlinear stochastic control systems. The technique
relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman
partial differential equation to a linear partial differential equation for a
class of problems with a particular constraint on the stochastic forcing. This
linear partial differential equation can then be relaxed to a linear
differential inclusion, allowing for relaxed solutions to be generated using
sum of squares programming. The resulting relaxed solutions are in fact
viscosity super/subsolutions, and by the maximum principle are pointwise upper
and lower bounds to the underlying value function, even for coarse polynomial
approximations. Furthermore, the pointwise upper bound is shown to be a
stochastic control Lyapunov function, yielding a method for generating
nonlinear controllers with pointwise bounded distance from the optimal cost
when using the optimal controller. These approximate solutions may be computed
with non-increasing error via a hierarchy of semidefinite optimization
problems. Finally, this paper develops a-priori bounds on trajectory
suboptimality when using these approximate value functions, as well as
demonstrates that these methods, and bounds, can be applied to a more general
class of nonlinear systems not obeying the constraint on stochastic forcing.
Simulated examples illustrate the methodology.Comment: Published in SIAM Journal of Control and Optimizatio
Design of generalized minimum variance controllers for nonlinear multivariable systems
The design and implementation of Generalized Minimum Variance control laws for nonlinear multivariable systems that can include severe nonlinearities is considered. The quadratic cost index minimised involves dynamically weighted error and nonlinear control signal costing terms. The aim here is to show the controller obtained is simple to design and implement. The features of the control law are explored. The controller obtained includes an internal model of the process and in one form is a nonlinear version of the Smith Predictor
New advances in H∞ control and filtering for nonlinear systems
The main objective of this special issue is to
summarise recent advances in H∞ control and filtering
for nonlinear systems, including time-delay, hybrid and
stochastic systems. The published papers provide new
ideas and approaches, clearly indicating the advances
made in problem statements, methodologies or applications
with respect to the existing results. The special
issue also includes papers focusing on advanced and
non-traditional methods and presenting considerable
novelties in theoretical background or experimental
setup. Some papers present applications to newly
emerging fields, such as network-based control and
estimation
GMV control of nonlinear multivariable systems
A Generalized Minimum Variance control law is derived for the control of nonlinear, possibly time-varying multivariable systems. The solution for the control law is original and was obtained in the time-domain using a simple operator representation of the process. The quadratic cost index involves both error and control signal costing terms. The controller obtained is simple to implement and includes an internal model of the process. In one form might be considered a nonlinear version of the Smith Predictor. However, unlike the Smith Predictor a stabilizing control law can be obtained even for some open-loop unstable processe
On general systems with network-enhanced complexities
In recent years, the study of networked control systems (NCSs) has gradually become an active research area due to the advantages of using networked media in many aspects such as the ease of maintenance and installation, the large flexibility and the low cost. It is well known that the devices in networks are mutually connected via communication cables that are of limited capacity. Therefore, some network-induced phenomena have inevitably emerged in the areas of signal processing and control engineering. These phenomena include, but are not limited to, network-induced communication delays, missing data, signal quantization, saturations, and channel fading. It is of great importance to understand how these phenomena influence the closed-loop stability and performance properties
Optimal control of ankle joint moment: Toward unsupported standing in paraplegia
This paper considers part of the problem of how to provide unsupported standing for paraplegics by feedback control. In this work our overall objective is to stabilize the subject by stimulation only of his ankle joints while the other joints are braced, Here, we investigate the problem of ankle joint moment control. The ankle plantarflexion muscles are first identified with pseudorandom binary sequence (PRBS) signals, periodic sinusoidal signals, and twitches. The muscle is modeled in Hammerstein form as a static recruitment nonlinearity followed by a linear transfer function. A linear-quadratic-Gaussian (LQG)-optimal controller design procedure for ankle joint moment was proposed based on the polynomial equation formulation, The approach was verified by experiments in the special Wobbler apparatus with a neurologically intact subject, and these experimental results are reported. The controller structure is formulated in such a way that there are only two scalar design parameters, each of which has a clear physical interpretation. This facilitates fast controller synthesis and tuning in the laboratory environment. Experimental results show the effects of the controller tuning parameters: the control weighting and the observer response time, which determine closed-loop properties. Using these two parameters the tradeoff between disturbance rejection and measurement noise sensitivity can be straightforwardly balanced while maintaining a desired speed of tracking. The experimentally measured reference tracking, disturbance rejection, and noise sensitivity are good and agree with theoretical expectations
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