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Register a new userRobust Estimator-Based Safety Verification: A Vector Norm Approach
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Added by
Binghan He
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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In this paper, we consider the problem of verifying safety constraint satisfaction for single-input single-output systems with uncertain transfer function coefficients. We propose a new type of barrier function based on a vector norm. This type of barrier function has a measurable upper bound without full state availability. An identifier-based estimator allows an exact bound for the uncertainty-based component of the barrier function estimate. Assuming that the system is safe initially allows an exponentially decreasing bound on the error due to the estimator transient. Barrier function and estimator synthesis is proposed as two convex sub-problems, exploiting linear matrix inequalities. The barrier function controller combination is then used to construct a safety backup controller. And we demonstrate the system in a simulation of a 1 degree-of-freedom human-exoskeleton interaction.
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Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive scenarios that are generated to represent uncertainties. In this paper, a novel scenario-based SMPC approach is proposed by actively learning a data-driven uncertainty set from available data with machine learning techniques. A systematical procedure is then proposed to further calibrate the uncertainty set, which gives appropriate probabilistic guarantee. The resulting data-driven uncertainty set is more compact than traditional norm-based sets, and can help reducing conservatism of control actions. Meanwhile, the proposed method requires less data samples than traditional scenario-based SMPC approaches, thereby enhancing the practicability of SMPC. Finally the optimal control problem is cast as a single-stage robust optimization problem, which can be solved efficiently by deriving the robust counterpart problem. The feasibility and stability issue is also discussed in detail. The efficacy of the proposed approach is demonstrated through a two-mass-spring system and a building energy control problem under uncertain disturbances.
In this paper, we study the norm-based robust (efficient) solutions of a Vector Optimization Problem (VOP). We define two kinds of non-ascent directions in terms of Clarkes generalized gradient and characterize norm-based robustness by means of the newly-defined directions. This is done under a basic Constraint Qualification (CQ). We extend the provided characterization to VOPs with conic constraints. Moreover, we derive a necessary condition for norm-based robustness utilizing a nonsmooth gap function.
We present a data-driven model predictive control (MPC) scheme for chance-constrained Markov jump systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that under sufficient decrease of the confidence levels, the resulting MPC scheme renders the closed-loop system mean-square stable with respect to the true-but-unknown distributions, while remaining less conservative than a fully robust approach. Finally, we show that the data-driven value function converges to its nominal counterpart as the sample size grows to infinity. We illustrate our approach on a numerical example.
We introduce a hybrid (discrete--continuous) safety controller which enforces strict state and input constraints on a system---but only acts when necessary, preserving transparent operation of the original system within some safe region of the state space. We define this space using a Min-Quadratic Barrier function, which we construct along the equilibrium manifold using the Lyapunov functions which result from linear matrix inequality controller synthesis for locally valid uncertain linearizations. We also introduce the concept of a barrier pair, which makes it easy to extend the approach to include trajectory-based augmentations to the safe region, in the style of LQR-Trees. We demonstrate our controller and barrier pair synthesis method in simulation-based examples.
In this paper, we introduce a sequential learning algorithm to address a probabilistically robust controller tuning problem. The algorithm leverages ideas from the areas of randomised algorithms and ordinal optimisation, which have both been proposed to find approximate solutions for difficult design problems in control. We formally prove that our algorithm yields a controller which meets a specified probabilisitic performance specification, assuming a Gaussian or near-Gaussian copula model for the controller performances. Additionally, we are able to characterise the computational requirement of the algorithm by using a lower bound on the distribution function of the algorithms stopping time. To validate our work, the algorithm is then demonstrated for the purpose of tuning model predictive controllers on a diesel engine air-path. It is shown that the algorithm is able to successfully tune a single controller to meet a desired performance threshold, even in the presence of uncertainty in the diesel engine model, that is inherent when a single representation is used across a fleet of vehicles.
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