244 research outputs found
Performance of Sensitivity based NMPC Updates in Automotive Applications
In this work we consider a half car model which is subject to unknown but
measurable disturbances. To control this system, we impose a combination of
model predictive control without stabilizing terminal constraints or cost to
generate a nominal solution and sensitivity updates to handle the disturbances.
For this approach, stability of the resulting closed loop can be guaranteed
using a relaxed Lyapunov argument on the nominal system and Lipschitz
conditions on the open loop change of the optimal value function and the stage
costs. For the considered example, the proposed approach is realtime applicable
and corresponding results show significant performance improvements of the
updated solution with respect to comfort and handling properties.Comment: 6 pages, 2 figure
Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems
Input-to-state stability of infinite-dimensional control systems
We develop tools for investigation of input-to-state stability (ISS) of
infinite-dimensional control systems. We show that for certain classes of
admissible inputs the existence of an ISS-Lyapunov function implies the
input-to-state stability of a system. Then for the case of systems described by
abstract equations in Banach spaces we develop two methods of construction of
local and global ISS-Lyapunov functions. We prove a linearization principle
that allows a construction of a local ISS-Lyapunov function for a system which
linear approximation is ISS. In order to study interconnections of nonlinear
infinite-dimensional systems, we generalize the small-gain theorem to the case
of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov
function for an entire interconnection, if ISS-Lyapunov functions for
subsystems are known and the small-gain condition is satisfied. We illustrate
the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page
Nominal model predictive control
5 p., to appear in Encyclopedia of Systems and Control, Tariq Samad, John Baillieul (eds.)International audienceModel Predictive Control is a controller design method which synthesizes a sampled data feedback controller from the iterative solution of open loop optimal control problems.We describe the basic functionality of MPC controllers, their properties regarding feasibility, stability and performance and the assumptions needed in order to rigorously ensure these properties in a nominal setting
Lazy Abstraction-Based Controller Synthesis
We present lazy abstraction-based controller synthesis (ABCS) for
continuous-time nonlinear dynamical systems against reach-avoid and safety
specifications. State-of-the-art multi-layered ABCS pre-computes multiple
finite-state abstractions of varying granularity and applies reactive synthesis
to the coarsest abstraction whenever feasible, but adaptively considers finer
abstractions when necessary. Lazy ABCS improves this technique by constructing
abstractions on demand. Our insight is that the abstract transition relation
only needs to be locally computed for a small set of frontier states at the
precision currently required by the synthesis algorithm. We show that lazy ABCS
can significantly outperform previous multi-layered ABCS algorithms: on
standard benchmarks, lazy ABCS is more than 4 times faster
Model order reduction approaches for infinite horizon optimal control problems via the HJB equation
We investigate feedback control for infinite horizon optimal control problems
for partial differential equations. The method is based on the coupling between
Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is
well-known that HJB equations suffer the so called curse of dimensionality and,
therefore, a reduction of the dimension of the system is mandatory. In this
report we focus on the infinite horizon optimal control problem with quadratic
cost functionals. We compare several model reduction methods such as Proper
Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati
equation based approach. Finally, we present numerical examples and discuss
several features of the different methods analyzing advantages and
disadvantages of the reduction methods
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