Questions tagged [optimal-control]

A tag for questions that relate to numerical approaches to optimal control of systems.

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108 views

Why researchers use MATLAB based YALMIP or CasADi for MPC?

I was looking at various research papers and most of the researchers use CasADi, YALMIP, MPCTools to implement MPC. My question is "Why researchers use MATLAB based YALMIP or CasADi for MPC ...
1 vote
0 answers
29 views

Non-Linear Distributed Delayed Kalman Filter

I have a system $\vec{x}_{i + 1} = \vec{x}_i + W_i$ where $W = N(\vec{\mu}, \Sigma)$. For some matrix $H_i$, let $y_i = H_i$ and let $z_i = y_i + R$. Where $R$ is some random variable. We are given $...
1 vote
1 answer
416 views

2-norm and infinty norm of a system in controls

How to compute 2-norm or infinity norm of following system? i am confused whether to calculate using simple matrix theory "where it don't regard for s domain" or H2 and H-infinty norm. ...
2 votes
1 answer
112 views

Objective function for PDE-constrained boundary control problem in cylindrical coordinates

I'm interested in solving a boundary control problem for an axisymmetric diffusion problem where diffusive fluxes only appear radially. The corresponding problem for a uni-dimensional slab can be ...
0 votes
0 answers
80 views

Automatic differentiation necessary for large optimal control problems?

I am investigating ways to solve an optimal control problem in an embedded way, preferably in Java. The system is modeled with triple integrator dynamics $u=\dddot{x}$ and solved with multiple ...
3 votes
1 answer
213 views

Which optimization algorithm to max a single parameter by searching a landscape of five parameters?

Background: We're operating a small betatron which makes use of a vacuum tube where electrons are accelerated circularly. First, they get injected (like inserted) and contracted (like squeezed). After ...
0 votes
1 answer
74 views

Solving numerically an Optimal Control Problem subject to a conservation law (transport equation)

I was wondering if there is some known way to solve the following optimal control problem \begin{align} \text{min }&\mathcal{J}(\rho,\nu)\\ \text{such that }&∂_t\rho(t, x) = − div_x(((K ∗ ρ)(t,...
4 votes
1 answer
3k views

Discrete-time Algebraic Riccati Equation (DARE) solver in C++

I need to use a Discrete-time Algebraic Riccati Equation (DARE) solver for an embedded controller (with limited processing power) in a research project and sadly, I can't find any implementation of it ...
1 vote
1 answer
4k views

What is difference between L2 norm and H2 Norm?

When someone refers 2-norm of system,L2 and H2 are used interchangeably by author and is rather confusing. Even the matlab has different functions for H-infinity norm and L-infinity norm. as shown in ...
4 votes
1 answer
306 views

What's the right choice of variable settings for setting up my optimal control problem?

This is a followup to my previous question here I have the following dynamical system, $\frac{d \phi}{dt} = -M^TDM\phi \tag{1}\label{1}$ $\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi \tag{2} \...
1 vote
0 answers
42 views

Optimality conditions for optimal control: BVP - DAE

I am solving an optimal control problem of the form $$ \min_u \qquad\int_0^T \langle u(t), u(t) \rangle \, \mathrm{d}t \\ s.t. \quad \dot{x} = \tilde{f}(x) + u, \quad x(0)=x_0 \\ \qquad \tilde{\Phi}(...
1 vote
0 answers
212 views

How to perform local sensitivity analysis for partial differential equations

I am looking for a way to do local sensitivity analysis for PDEs, preferably in Python. I get the impression that discretizing the equation then treating it as an ODE could work; however, would that ...
5 votes
1 answer
109 views

What are systematic ways of approximating a non-smooth (non-continuously differentiable) system dynamic to be n-smooth?

I have a system dynamic that is non-smooth because it has several signum and absolute value functions in it (three-tank level control). I can obviously choose different sigmoid functions to ...
6 votes
1 answer
190 views

zero terminal value of the adjoint based optimal control

I have been pondering about this issue for some time... Say, I want to minimize a costfunctional $$ \tilde J(u) = J(v(u),u) = \frac 12 \int_0^T (v-v_0)^2 + \alpha u^2 dt $$ subject to $$ \dot v = v^2 ...
1 vote
1 answer
412 views

Approximation Error in a Finite Difference Approximation of the Square of Derivative

First Part: (First-order derivative) Assuming $f$ is an infinitely differential function everywhere, the Taylor series of $f(x + h)$ at $x$ is \begin{align}\tag{1} f(x + h) = f(x) + hf'(x) + \frac{1}...
0 votes
1 answer
215 views

Numerical solution of non-linear first order partial differential equation (HJB)

I am trying to solve a simple optimal control problem using the Hamilton-Jacobi-Bellman equation, numerically in Python. This is proving to be rather difficult as I end up having to solve the ...
3 votes
0 answers
47 views

Guide for finite-difference schemes for Hamilton-Jacobi-Bellman Equations

I need to solve a simple, low-dimensional Hamilton-Jacobi-Bellman equation. Is there a simple guide for doing this numerically using finite-difference schemes? I found a few research articles ...
1 vote
0 answers
17 views

Procedure to identify characteristic properties of unknown functions in a DAE model

I have a system of 1st order odes given by $$ \dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t) $$ They are constrained by an algebraic equation ...
1 vote
0 answers
65 views

scaling in discretized PDE system

I want to solve the following system via Matlab $\Omega=(0,1)^2$ $$\Delta y=\frac{1}{\alpha} p$$ $$ -\Delta p= y -1 $$ $$p|_{\partial \Omega}=0,~y|_{\partial \Omega}=0$$ using ...
1 vote
1 answer
217 views

proper derivation of a functional for a time dependent parameter estimation problem

Following my previous question and its answer, after some reading of the advised books, I'm still confused about how to get the derivative of the functional to find the best parameter of my reaction ...
1 vote
1 answer
1k views

Direct multiple shooting (numerical optimal control)

Please, I am currently implementing direct multiple shooting methods* and I need one simple but fundamental concept answered: When I want to provide not only objective function value (the result of ...
1 vote
1 answer
206 views

Robust/Tested Solver for incompressible 2D Euler (Fluid dynamics) Equation

I am trying to locate suitable computational algorithms for a optimization problem that requires repeated solution of transient 2D incompressible Euler equation on a 2D domain (say rectangular). My ...
3 votes
0 answers
212 views

Optimal Control using Dynamic Programming - Optimizing for Furthest Distance

So I have been investigating a problem to get a glider with control of its elevator to fly as far as possible from any given initial state. To keep this simple, we will view this in 2D space with the ...
3 votes
1 answer
726 views

Position Estimation using 2D multilateration for non-intersecting distances

I am trying to estimate the position of a point $P$ in Matlab. I have $n$ access points (AP) at known positions ($n>2$) as well as the distances to the point $P$ from each AP. These distances all ...
1 vote
1 answer
278 views

GAMS Optimization

I am writing a GAMS program where I am interested in using the value of a variable as a condition inside an another equation. Let's say I have two equations with two variables, $g_1(t)$ and $g_2(t)$, ...
1 vote
0 answers
53 views

A stable method for solving monontoe HJB equation

I am considering solving HJB equation of the form $$ v_t=g(a(x)v_x),\quad x\in \mathbb{R}, t>0, $$ with initial condition $v(0)=v_0$. Here $g:\mathbb{R}\to \mathbb{R}$ is Lipschitz and monotone ...
1 vote
1 answer
87 views

Using two reference values for a scalar variable: What's the name of this type of problem?

I don't really know where to ask this one... In fact, I am not sure I can define it properly. Here goes... Let's say I take measurements. In order to "normalize" these measurements, I divide their ...
1 vote
0 answers
49 views

Help formulating/finding the general class of this problem

Imagine a bus serving a line with N stations. Each station, $i, i=1,…N$, has $s_{ij}$ passengers that want to board the bus to go to $j$, $\forall j \neq i$. (one direction). So there are $\sum_j s_{...
2 votes
0 answers
79 views

Convergence of KKT equations for discrete parameter estimation problems

Consider a discrete constrained optimization problem: $$ \mathbf{q}_*^h= \arg \min {\cal J}^h(\mathbf{x}^h[\mathbf{q}^h],\mathbf{q}^h) $$ subject to the (weak-form) constraint $$ F^h[\mathbf{x}^h(\...
1 vote
0 answers
82 views

How to speed convergence when optimizing a linear objective with nonlinear constraints?

I'm trying to learn how to do optimal rocket trajectory planning. I have a process that works but it converges very slowly; I'm looking for help to understand how to speed that up. The optimal ...
1 vote
0 answers
69 views

Comparison between of higher order interpolations

A while ago I came up with an algorithm which can be used to numerically solve optimal control problems, which basically came down to discretizing the control input $u(t)$ and interpolating this to ...
0 votes
1 answer
294 views

Strict Feasibility in Interior Point Methods

As we know, in the interior point methods, all the iterates have to be strictly feasible. I implemented an affine scaling interior point for nonlinear objective functions. For small examples (2D), it ...
5 votes
3 answers
189 views

Algorithms for radiation treatment planning

I have a medical physics problem - I want to maximise the dose absorbed by a brain tumour whilst minimising the dose in the rest of the brain, especially certain organs, such as the pituitary gland, ...
5 votes
0 answers
89 views

numerical solver for stochastic optimal control problems

can any one recommend numerical solver (c/c++ library preferred) for stochastic optimal control problems? For deterministic optimal control I found something like that: http://abs-5.me.washington.edu/...
6 votes
0 answers
106 views

Benchmarks or generic configurations for optimal flow control

I am about to test my algorithms for solving optimal control problems of type: Find an input $u$, such that for a time interval $(0,T]$ the cost functional $$J(v,u) = \mathcal M(v(T)) + \int_0^T\...