# Questions tagged [optimal-control]

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

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0answers
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### 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 ...
1answer
94 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 ...
1answer
68 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}...
0answers
295 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 ...
1answer
61 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 ...
0answers
36 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 ...
0answers
16 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 ...
0answers
57 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 ...
1answer
193 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 ...
1answer
164 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 ...
0answers
199 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 ...
1answer
506 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 ...
1answer
159 views

0answers
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### 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 ...
0answers
54 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 ...
1answer
533 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 ...
1answer
192 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 ...
3answers
174 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, ...
0answers
69 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/...
0answers
92 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\...