Optimal control

By Victor M. Becerra. Scholarpedia, 2008

3,264 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e982d77087212440ef9f80b3f33e497888acd7e7

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In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Local null controllability of the three-dimensional Navier–Stokes system with a distributed control having two vanishing components (2012, background): “It is well-known (see for example [16], or [23]) that if this linear system were null controllable (with, in addition, an arbitrary source term in a suitable space), then applying an inverse mapping theorem (for example the one presented in [2]) in some relevant weighted spaces, we would obtain that”
Decentralized Cooperative Aerial Surveillance Using Fixed-Wing Miniature UAVs (2006, background): “In our example problem, a possible coordination objective is given by the linear quadratic regulator equation [53]”
On the benefits of the LDLT factorization for large-scale differential matrix equation solvers (2015, neutral): “, [36]) u = −R−1BTX(t)Ex(t) = −K(t)x(t).”
Motion Planning (2008, positive): “We recall in Section 2 its basic version which we will use, and refer to classical books in control theory, like [1], [4], and [7], for its quite delicate proof.”
Kinodynamic RRT*: Asymptotically optimal motion planning for robots with linear dynamics (2013, methodology): “It is known from [15] what the optimal control policy is in case a fixed arrival time τ is given, as we review in Section IV-A.”
Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, background): “We refer the reader to textbooks such as [1,16,18,19,29,33,38,49,51,52,54] for theoretical results and/or practical applications, essentially for dynamical systems described by ordinary differential equations.”
Formalizing the Generalization-Forgetting Trade-off in Continual Learning (2021, methodology): “We will first recast the problem using tools from dynamic programming [29], specifically Bellman’s principle of optimality, and derive a difference equation that summarizes the complete dynamics for the CL problem.”
Multi-agent differential graphical games (2011, methodology): “Employing the stationarity condition (12) (Lewis & Syrmos, 1995) one obtains the control policies ui = ui(Vi) ≡ −(di + gi)R−1ii B T i ∂Vi ∂δi ≡ −hi(pi).”
Adaptive optimal control for continuous-time linear systems based on policy iteration (2009, positive): “The solution of this optimal control problem, determined by Bellman's optimality principle (Lewis & Syrmos, 1995 ), is given by u(t) = −Kx(t) with K = R −1 B T P (4) where the matrix P is the unique positive definite solution of the Algebraic Riccati Equation (ARE) A T P + PA − PBR −1 B T P + Q = 0.”
Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions (2015, positive): “5 in [1]), there is a sufficiently small α0 > 0 such that for all α ∈ (0, α0] the solution x̃α(·) of (22) exists on [0, τ ] and ‖x̃α(0)−x∗(0)‖ < β.”
Distributed optimal control of multiple systems (2010, background): “The proof of the result can be found in many textbooks, such as Anderson and Moore (1971) and Lewis and Syrmos (1995).”
Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton-Jacobi equations (2011, background): “To justify this, the matrix M is written in compact form as .10) where in order to be positive definite the following properties (Lewis & Syrmos, 1995) must hold (a) q 1 + q 2 > 0.”
A review of pseudospectral optimal control: From theory to flight (2012, positive): “These practical di ﬃ culties are not the topic of typical mathematical research because even if all these challenges are met, there is the overhanging doom of the curse of dimensionality coupled with the issues related to the nondi ﬀ erentiability of V [20].”
The turnpike property in finite-dimensional nonlinear optimal control (2014, positive): “As it is by now well known, such an assumption is automatically satisfied under slight conditions for many classes of optimal control problems (see [19, 45]), or under appropriate controllability assumptions (see [8, 54]).”
Secure Cooperative Event-Triggered Control of Linear Multiagent Systems Under DoS Attacks (2020, background): “For clarity in the subsequent stability analysis, deﬁne B = √ Here, P > 0 is the solution to algebraic Riccati equation (ARE): P A + A T P − PB R − 1 B T P + Q = 0 where Q > 0 and R > 0 are two design positive deﬁnite matrices [37].”
Needle Variations in Infinite-Horizon Optimal Control (2014, neutral): “6 in [1]), the following representation holds:”