98 research outputs found
Necessary and sufficient conditions for robust gain scheduling
Recent results in the design of controllers for parameter dependent systems are extended to systems with plant uncertainty. The solution takes the form of an affine matrix
inequality (AMI), which is both a necessary and sufficient condition for the posed problem to have a solution. The results in this paper may be used for the design of gain scheduled controllers for a class of uncertain systems
LMI approach to mixed performance objective controllers: application to Robust β2 Synthesis
The problem of synthesizing a controller for plants subject to arbitrary, finite energy disturbances and white noise disturbances via Linear Matrix Inequalities (LMIs) is presented. This is achieved by considering white noise disturbances as belonging to a constrained set in β2. In the case of where only white noise disturbances are present, the procedure reduces to standard β2 synthesis. When arbitrary, finite energy disturbances are also present, the procedure may be used to synthesize general mixed performance objective controllers, and for certain cases, Robust β2 controllers
ββ optimization with spatial constraints
A generalized ββ synthesis problem where non-euclidian spatial norms on the disturbances and output error are used is posed and solved. The solution takes the form of a linear matrix inequality. Some problems which fall into this class are presented. In particular, solutions are presented to two problems: a variant of ββ synthesis where norm constraints on each component of the disturbance can be imposed, and synthesis for a certain class of robust performance problems
Generalized β2 synthesis
A framework for optimal controller design with generalized β2 objectives is presented. The allowable disturbances are constrained to be in a pre-specified set; the design objective is to ensure that the resulting output errors do not belong to another pre-specified set. The solution takes the form of an affine matrix inequality (AMI), which is both a necessary
and sufficient condition for the posed problem to have a solution. In the simplest case, the resulting optimization reduces to standard ββ synthesis
H-Infinity Optimal Interconnections
In this paper, a general ββ problem for continuous time, linear time invariant systems is formulated and solved in a behavioral framework. This general formulation, which includes standard ββ optimization as a special case, provides added freedom in the design of sub-optimal compensators, and can in fact be viewed as a means of designing optimal systems. In particular, the formulation presented allows for singular interconnections, which naturally occur when interconnecting first principles models
Distributed Control of Spatially Reversible Interconnected Systems with Boundary Conditions
We present a class of spatially interconnected systems with boundary conditions that have close links with their spatially invariant extensions. In particular, well-posedness, stability, and performance of the extension imply the same characteristics for the actual, finite extent system. In turn, existing synthesis methods for control of spatially invariant systems can be extended to this class. The relation between the two kinds of systems is proved using ideas based on the "method of images" of partial differential equations theory and uses symmetry properties of the interconnection as a key tool
On the Approximation of Constrained Linear Quadratic Regulator Problems and their Application to Model Predictive Control - Supplementary Notes
By parametrizing input and state trajectories with basis functions different
approximations to the constrained linear quadratic regulator problem are
obtained. These notes present and discuss technical results that are intended
to supplement a corresponding journal article. The results can be applied in a
model predictive control context.Comment: 19 pages, 1 figur
Approximation of Continuous-Time Infinite-Horizon Optimal Control Problems Arising in Model Predictive Control - Supplementary Notes
These notes present preliminary results regarding two different
approximations of linear infinite-horizon optimal control problems arising in
model predictive control. Input and state trajectories are parametrized with
basis functions and a finite dimensional representation of the dynamics is
obtained via a Galerkin approach. It is shown that the two approximations
provide lower, respectively upper bounds on the optimal cost of the underlying
infinite dimensional optimal control problem. These bounds get tighter as the
number of basis functions is increased. In addition, conditions guaranteeing
convergence to the cost of the underlying problem are provided.Comment: Supplementary notes, 10 page
- β¦