591 research outputs found
A Unified Framework for the Study of Anti-Windup Designs
We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: "Design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance". The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. It is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model. The actual analysis of stability and performance, and robustness issues are problems in their own right and hence not detailed here. The main result is the unification of existing schemes for AWBT compensation under a general framework
A Conic Sector-Based Methodology for Nonlinear Control Design
A design method is presented for the analysis and synthesis of robust nonlinear controllers for chemical engineering systems. The method rigorously treats the effect of unmeasured disturbances and unmodeled dynamics on the stability and performance properties of a nonlinear system. The results utilise new extensions of structured singular value theory for analysis and recent synthesis results for approximate linearisation
Multivariable Anti-Windup and Bumpless Transfer: A General Theory
A general theory is developed to address the anti-windup/bumpless transfer (AWBT) problem. Analysis results applicable to any linear time invariant system subject to plant input limitations and substitutions are presented. Quantitative performance objectives for AWBT compensation are outlined and several proposed AWBT methods are evaluated in light of these objectives. A synthesis procedure which highlights the performance trade-offs for AWBT compensation design is outlined
Robust Controller Design for a Nonlinear CSTR
A design methodology is presented for the analysis and synthesis of robust linear controllers for a nonlinear continuous stirred tank reactor. Regions are defined in the phase plane in which the maintenance of robust stability and the achievement of robust performance levels are guaranteed. The results are based upon new extensions of the structured singular value theory to a class of nonlinear and time-varying systems
Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming
There has been an increasing interest in using neural networks in closed-loop
control systems to improve performance and reduce computational costs for
on-line implementation. However, providing safety and stability guarantees for
these systems is challenging due to the nonlinear and compositional structure
of neural networks. In this paper, we propose a novel forward reachability
analysis method for the safety verification of linear time-varying systems with
neural networks in feedback interconnection. Our technical approach relies on
abstracting the nonlinear activation functions by quadratic constraints, which
leads to an outer-approximation of forward reachable sets of the closed-loop
system. We show that we can compute these approximate reachable sets using
semidefinite programming. We illustrate our method in a quadrotor example, in
which we first approximate a nonlinear model predictive controller via a deep
neural network and then apply our analysis tool to certify finite-time
reachability and constraint satisfaction of the closed-loop system
Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks
Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is
useful in many applications ranging from robustness certification of
classifiers to stability analysis of closed-loop systems with reinforcement
learning controllers. Existing methods in the literature for estimating the
Lipschitz constant suffer from either lack of accuracy or poor scalability. In
this paper, we present a convex optimization framework to compute guaranteed
upper bounds on the Lipschitz constant of DNNs both accurately and efficiently.
Our main idea is to interpret activation functions as gradients of convex
potential functions. Hence, they satisfy certain properties that can be
described by quadratic constraints. This particular description allows us to
pose the Lipschitz constant estimation problem as a semidefinite program (SDP).
The resulting SDP can be adapted to increase either the estimation accuracy (by
capturing the interaction between activation functions of different layers) or
scalability (by decomposition and parallel implementation). We illustrate the
utility of our approach with a variety of experiments on randomly generated
networks and on classifiers trained on the MNIST and Iris datasets. In
particular, we experimentally demonstrate that our Lipschitz bounds are the
most accurate compared to those in the literature. We also study the impact of
adversarial training methods on the Lipschitz bounds of the resulting
classifiers and show that our bounds can be used to efficiently provide
robustness guarantees
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