14,716 research outputs found
Linear Control Theory with an ℋ∞ Optimality Criterion
This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods
New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems
This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use
Coprime Factor Reduction of H-infinity Controllers
We consider the efficient solution of the coprime factorization based H infinity controller approximation problems by using frequency-weighted balancing related model reduction approaches. It is shown that for a class of frequency-weighted performance preserving coprime factor reduction as well as for a relative error coprime factor reduction method, the computation of the frequency-weighted controllability and observability grammians can be done by solving Lyapunov equations of the order of the controller. The new approach can be used in conjunction with accuracy enhancing square-root and balancing-free techniques developed for the balancing related coprime factors based model reduction
Frequency-Weighted Model Reduction with Applications to Structured Models
In this paper, a frequency-weighted extension of a
recently proposed model reduction method for linear systems
is presented. The method uses convex optimization and can be
used both with sample data and exact models. We also obtain
bounds on the frequency-weighted error. The method is combined
with a rank-minimization heuristic to approximate multiinput–
multi-output systems.We also present two applications—
environment compensation and simplification of interconnected
models — where we argue the proposed methods are useful
A Characterization of all Solutions to the Four Block General Distance Problem
All solutions to the four block general distance problem which arises in H^∞ optimal control are characterized. The procedure is to embed the original problem in an all-pass matrix which is constructed. It is then shown that part of this all-pass matrix acts as a generator of all solutions. Special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all-pass
transfer functions. As an application, necessary and sufficient conditions are found for the existence of an H^∞ optimal controller. Following that, a descriptor representation of all solutions is derived
Stochastic Model Predictive Control for Autonomous Mobility on Demand
This paper presents a stochastic, model predictive control (MPC) algorithm
that leverages short-term probabilistic forecasts for dispatching and
rebalancing Autonomous Mobility-on-Demand systems (AMoD, i.e. fleets of
self-driving vehicles). We first present the core stochastic optimization
problem in terms of a time-expanded network flow model. Then, to ameliorate its
tractability, we present two key relaxations. First, we replace the original
stochastic problem with a Sample Average Approximation (SAA), and characterize
the performance guarantees. Second, we separate the controller into two
separate parts to address the task of assigning vehicles to the outstanding
customers separate from that of rebalancing. This enables the problem to be
solved as two totally unimodular linear programs, and thus easily scalable to
large problem sizes. Finally, we test the proposed algorithm in two scenarios
based on real data and show that it outperforms prior state-of-the-art
algorithms. In particular, in a simulation using customer data from DiDi
Chuxing, the algorithm presented here exhibits a 62.3 percent reduction in
customer waiting time compared to state of the art non-stochastic algorithms.Comment: Submitting to the IEEE International Conference on Intelligent
Transportation Systems 201
Linear Hamilton Jacobi Bellman Equations in High Dimensions
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal
solution to large classes of control problems. Unfortunately, this generality
comes at a price, the calculation of such solutions is typically intractible
for systems with more than moderate state space size due to the curse of
dimensionality. This work combines recent results in the structure of the HJB,
and its reduction to a linear Partial Differential Equation (PDE), with methods
based on low rank tensor representations, known as a separated representations,
to address the curse of dimensionality. The result is an algorithm to solve
optimal control problems which scales linearly with the number of states in a
system, and is applicable to systems that are nonlinear with stochastic forcing
in finite-horizon, average cost, and first-exit settings. The method is
demonstrated on inverted pendulum, VTOL aircraft, and quadcopter models, with
system dimension two, six, and twelve respectively.Comment: 8 pages. Accepted to CDC 201
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