14,350 research outputs found
A New Contraction-Based NMPC Formulation Without Stability-Related terminal Constraints
Contraction-Based Nonlinear Model Predictive Control (NMPC) formulations are
attractive because of the generally short prediction horizons they require and
the needless use of terminal set computation that are commonly necessary to
guarantee stability. However, the inclusion of the contraction constraint in
the definition of the underlying optimization problem often leads to non
standard features such as the need for multi-step open-loop application of
control sequences or the use of multi-step memorization of the contraction
level that may induce unfeasibility in presence of unexpected disturbance. This
paper proposes a new formulation of contraction-based NMPC in which no
contraction constraint is explicitly involved. Convergence of the resulting
closed-loop behavior is proved under mild assumptions.Comment: accepted in short version IFAC Nolcos 2016. submitted to Automatica
as a technical communiqu
Robust predictive feedback control for constrained systems
A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model
Robust Constrained Model Predictive Control using Linear Matrix Inequalities
The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented
A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control
This paper introduces a family of iterative algorithms for unconstrained
nonlinear optimal control. We generalize the well-known iLQR algorithm to
different multiple-shooting variants, combining advantages like
straight-forward initialization and a closed-loop forward integration. All
algorithms have similar computational complexity, i.e. linear complexity in the
time horizon, and can be derived in the same computational framework. We
compare the full-step variants of our algorithms and present several simulation
examples, including a high-dimensional underactuated robot subject to contact
switches. Simulation results show that our multiple-shooting algorithms can
achieve faster convergence, better local contraction rates and much shorter
runtimes than classical iLQR, which makes them a superior choice for nonlinear
model predictive control applications.Comment: 8 page
Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)
A new framework is developed for control of constrained nonlinear systems
with structured parametric uncertainties. Forward invariance of a safe set is
achieved through online parameter adaptation and data-driven model estimation.
The new adaptive data-driven safety paradigm is merged with a recent adaptive
control algorithm for systems nominally contracting in closed-loop. This
unification is more general than other safety controllers as closed-loop
contraction does not require the system be invertible or in a particular form.
Additionally, the approach is less expensive than nonlinear model predictive
control as it does not require a full desired trajectory, but rather only a
desired terminal state. The approach is illustrated on the pitch dynamics of an
aircraft with uncertain nonlinear aerodynamics.Comment: Added aCBF non-Lipschitz example and discussion on approach
implementatio
Model Predictive Control meets robust Kalman filtering
Model Predictive Control (MPC) is the principal control technique used in
industrial applications. Although it offers distinguishable qualities that make
it ideal for industrial applications, it can be questioned its robustness
regarding model uncertainties and external noises. In this paper we propose a
robust MPC controller that merges the simplicity in the design of MPC with
added robustness. In particular, our control system stems from the idea of
adding robustness in the prediction phase of the algorithm through a specific
robust Kalman filter recently introduced. Notably, the overall result is an
algorithm very similar to classic MPC but that also provides the user with the
possibility to tune the robustness of the control. To test the ability of the
controller to deal with errors in modeling, we consider a servomechanism system
characterized by nonlinear dynamics
Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization
This paper proposes an algorithmic framework for solving parametric
optimization problems which we call adjoint-based predictor-corrector
sequential convex programming. After presenting the algorithm, we prove a
contraction estimate that guarantees the tracking performance of the algorithm.
Two variants of this algorithm are investigated. The first one can be used to
solve nonlinear programming problems while the second variant is aimed to treat
online parametric nonlinear programming problems. The local convergence of
these variants is proved. An application to a large-scale benchmark problem
that originates from nonlinear model predictive control of a hydro power plant
is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure
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