148,478 research outputs found
Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control
Today's fast linear algebra and numerical optimization tools have pushed the
frontier of model predictive control (MPC) forward, to the efficient control of
highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated
that exact optimal control law can be computed, e.g., by mixed-integer
programming (MIP) under piecewise-affine (PWA) system models. Despite the
elegant theory, online solving hybrid MPC is still out of reach for many
applications. We aim to speed up MIP by combining geometric insights from
hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start
techniques. Following a line of work in approximate explicit MPC, the proposed
learning-control algorithm, LNMS, gains computational advantage over MIP at
little cost and is straightforward for practitioners to implement
Learning an Approximate Model Predictive Controller with Guarantees
A supervised learning framework is proposed to approximate a model predictive
controller (MPC) with reduced computational complexity and guarantees on
stability and constraint satisfaction. The framework can be used for a wide
class of nonlinear systems. Any standard supervised learning technique (e.g.
neural networks) can be employed to approximate the MPC from samples. In order
to obtain closed-loop guarantees for the learned MPC, a robust MPC design is
combined with statistical learning bounds. The MPC design ensures robustness to
inaccurate inputs within given bounds, and Hoeffding's Inequality is used to
validate that the learned MPC satisfies these bounds with high confidence. The
result is a closed-loop statistical guarantee on stability and constraint
satisfaction for the learned MPC. The proposed learning-based MPC framework is
illustrated on a nonlinear benchmark problem, for which we learn a neural
network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter
Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis
Even with impressive advances in automated formal methods, certain problems
in system verification and synthesis remain challenging. Examples include the
verification of quantitative properties of software involving constraints on
timing and energy consumption, and the automatic synthesis of systems from
specifications. The major challenges include environment modeling,
incompleteness in specifications, and the complexity of underlying decision
problems.
This position paper proposes sciduction, an approach to tackle these
challenges by integrating inductive inference, deductive reasoning, and
structure hypotheses. Deductive reasoning, which leads from general rules or
concepts to conclusions about specific problem instances, includes techniques
such as logical inference and constraint solving. Inductive inference, which
generalizes from specific instances to yield a concept, includes algorithmic
learning from examples. Structure hypotheses are used to define the class of
artifacts, such as invariants or program fragments, generated during
verification or synthesis. Sciduction constrains inductive and deductive
reasoning using structure hypotheses, and actively combines inductive and
deductive reasoning: for instance, deductive techniques generate examples for
learning, and inductive reasoning is used to guide the deductive engines.
We illustrate this approach with three applications: (i) timing analysis of
software; (ii) synthesis of loop-free programs, and (iii) controller synthesis
for hybrid systems. Some future applications are also discussed
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