89,766 research outputs found
On Optimal Input Design for Feed-forward Control
This paper considers optimal input design when the intended use of the
identified model is to construct a feed-forward controller based on measurable
disturbances. The objective is to find a minimum power excitation signal to be
used in system identification experiment, such that the corresponding
model-based feed-forward controller guarantees, with a given probability, that
the variance of the output signal is within given specifications. To start
with, some low order model problems are analytically solved and fundamental
properties of the optimal input signal solution are presented. The optimal
input signal contains feed-forward control and depends of the noise model and
transfer function of the system in a specific way. Next, we show how to apply
the partial correlation approach to closed loop optimal experiment design to
the general feed-forward problem. A framework for optimal input signal design
for feed-forward control is presented and numerically evaluated on a
temperature control problem
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
State-space approach to nonlinear predictive generalized minimum variance control
A Nonlinear Predictive Generalized Minimum Variance (NPGMV) control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time-domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process but because of the assumed structure of the system the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well known GPC controller
Motion Planning of Uncertain Ordinary Differential Equation Systems
This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems.
Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs.
The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space
Estimator Selection: End-Performance Metric Aspects
Recently, a framework for application-oriented optimal experiment design has
been introduced. In this context, the distance of the estimated system from the
true one is measured in terms of a particular end-performance metric. This
treatment leads to superior unknown system estimates to classical experiment
designs based on usual pointwise functional distances of the estimated system
from the true one. The separation of the system estimator from the experiment
design is done within this new framework by choosing and fixing the estimation
method to either a maximum likelihood (ML) approach or a Bayesian estimator
such as the minimum mean square error (MMSE). Since the MMSE estimator delivers
a system estimate with lower mean square error (MSE) than the ML estimator for
finite-length experiments, it is usually considered the best choice in practice
in signal processing and control applications. Within the application-oriented
framework a related meaningful question is: Are there end-performance metrics
for which the ML estimator outperforms the MMSE when the experiment is
finite-length? In this paper, we affirmatively answer this question based on a
simple linear Gaussian regression example.Comment: arXiv admin note: substantial text overlap with arXiv:1303.428
A Probabilistic Approach to Robust Optimal Experiment Design with Chance Constraints
Accurate estimation of parameters is paramount in developing high-fidelity
models for complex dynamical systems. Model-based optimal experiment design
(OED) approaches enable systematic design of dynamic experiments to generate
input-output data sets with high information content for parameter estimation.
Standard OED approaches however face two challenges: (i) experiment design
under incomplete system information due to unknown true parameters, which
usually requires many iterations of OED; (ii) incapability of systematically
accounting for the inherent uncertainties of complex systems, which can lead to
diminished effectiveness of the designed optimal excitation signal as well as
violation of system constraints. This paper presents a robust OED approach for
nonlinear systems with arbitrarily-shaped time-invariant probabilistic
uncertainties. Polynomial chaos is used for efficient uncertainty propagation.
The distinct feature of the robust OED approach is the inclusion of chance
constraints to ensure constraint satisfaction in a stochastic setting. The
presented approach is demonstrated by optimal experimental design for the
JAK-STAT5 signaling pathway that regulates various cellular processes in a
biological cell.Comment: Submitted to ADCHEM 201
NGMV control of delayed piecewise affine systems
A Nonlinear Generalized Minimum Variance (NGMV) control algorithm is introduced for the control of piecewise affine (PWA) systems. Under some conditions, discrete-time PWA systems can be transferred into an equivalent state-dependent nonlinear system form. The equivalent state-dependent systems maintain the hybrid nature of the original PWA systems and include both the discrete and continuous signals in one general description. In a more general way, the process is assumed to include common delays in input or output channels of magnitude k. Then the NGMV control strategy [1] can be applied. The NGMV controller is related to a well-known and accepted solution for time delay systems (Smith Predictor) but has the advantage that it may stabilize open-loop unstable processes [2]
On the Design of LQR Kernels for Efficient Controller Learning
Finding optimal feedback controllers for nonlinear dynamic systems from data
is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful
framework for direct controller tuning from experimental trials. For selecting
the next query point and finding the global optimum, BO relies on a
probabilistic description of the latent objective function, typically a
Gaussian process (GP). As is shown herein, GPs with a common kernel choice can,
however, lead to poor learning outcomes on standard quadratic control problems.
For a first-order system, we construct two kernels that specifically leverage
the structure of the well-known Linear Quadratic Regulator (LQR), yet retain
the flexibility of Bayesian nonparametric learning. Simulations of uncertain
linear and nonlinear systems demonstrate that the LQR kernels yield superior
learning performance.Comment: 8 pages, 5 figures, to appear in 56th IEEE Conference on Decision and
Control (CDC 2017
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