344 research outputs found
Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria
A novel state dependent control approach for discrete-time nonlinear systems with general performance criteria is presented. This controller is robust for unstructured model uncertainties, resilient against bounded feedback control gain perturbations in achieving optimality for general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state dependent linear matrix inequality at each time step, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control to provide a novel robust control design. The effectiveness of the proposed technique is demonstrated by simulation of the control of inverted pendulum
Integral and measure-turnpike properties for infinite-dimensional optimal control systems
We first derive a general integral-turnpike property around a set for
infinite-dimensional non-autonomous optimal control problems with any possible
terminal state constraints, under some appropriate assumptions. Roughly
speaking, the integral-turnpike property means that the time average of the
distance from any optimal trajectory to the turnpike set con- verges to zero,
as the time horizon tends to infinity. Then, we establish the measure-turnpike
property for strictly dissipative optimal control systems, with state and
control constraints. The measure-turnpike property, which is slightly stronger
than the integral-turnpike property, means that any optimal (state and control)
solution remains essentially, along the time frame, close to an optimal
solution of an associated static optimal control problem, except along a subset
of times that is of small relative Lebesgue measure as the time horizon is
large. Next, we prove that strict strong duality, which is a classical notion
in optimization, implies strict dissipativity, and measure-turnpike. Finally,
we conclude the paper with several comments and open problems
Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets
Imitation learning enables the synthesis of controllers for complex
objectives and highly uncertain plant models. However, methods to provide
stability guarantees to imitation learned controllers often rely on large
amounts of data and/or known plant models. In this paper, we explore an
input-output (IO) stability approach to dissipative imitation learning, which
achieves stability with sparse data sets and with little known about the plant
model. A closed-loop stable dynamic output feedback controller is learned using
expert data, a coarse IO plant model, and a new constraint to enforce
dissipativity on the learned controller. While the learning objective is
nonconvex, iterative convex overbounding (ICO) and projected gradient descent
(PGD) are explored as methods to successfully learn the controller. This new
imitation learning method is applied to two unknown plants and compared to
traditionally learned dynamic output feedback controller and neural network
controller. With little knowledge of the plant model and a small data set, the
dissipativity constrained learned controller achieves closed loop stability and
successfully mimics the behavior of the expert controller, while other methods
often fail to maintain stability and achieve good performance
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