Tagged Questions
1
vote
0answers
36 views
How do I solve an optimal control problem when the state and control are multiplied?
Suppose I have the following objective function
$$
R = \sum_t^T x_tu_t + ku_t^2
$$
subject to
$$
\Delta x_t = m u_t + n x_t
$$
where $x_t$ is the state and $u_t$ is the control. $x_0$ is known.
How ...
0
votes
1answer
31 views
Understanding the Hamiltonian function
Based on this function:
$$\text{max} \int_0^2(-2tx-u^2) \, dt$$
We know that $$(1) \;-1 \leq u \leq 1, \; \; \; (2) \; \dot{x}=2u, \; \; \; (3) \; x(0)=1, \; \; \; \text{x(2) is free}$$
I can ...
3
votes
1answer
58 views
minimization problem on differential equations - optimal control
I am trying to minimize an time-integral of a linear function with respect to differential equations. The problem is formally defined as follows:
Given $\lambda< \mu_1, \mu_2$ fixed ...
2
votes
0answers
26 views
How verification argument really works?
Let $C(u,s)$ be cost functional for an admissible control $u$ with initial state of the system being $s$.
Our aim is the solution of the following problem:
$$\inf_u E(C(u,s))$$
We defined the value ...
3
votes
2answers
131 views
Solution of a Sylvester equation?
I'd like to solve $AX -BX + XC = D$, for the matrix $X$, where all matrices have real entries and $X$ is a rectangular matrix, while $B$ and $C$ are symmetric matrices and $A$ is formed by an outer ...
2
votes
1answer
42 views
Verification for maximum principle
Given optimal control problem
$$
\dot x = f(t,x(t),u(t)), \quad x(0) = x_0,\\
J(u) = \int_0^T f^0(t,x(t),u(t))dt \to \min,
$$
we can apply Pontryagin's maximum principle to get a necessary condition ...
2
votes
1answer
56 views
How can I solve this control problem?
Consider this control problem in continuous time, known as Representative Agent Model in macroeconomics:
$$ \max_{c_t,t\ge 0}\int_{0}^{\infty}e^{-\rho t}\ln(c_t)\, \mathrm{d}t,~~~\rho\in (0,1) $$
...
0
votes
0answers
17 views
How to find and define the objective for control system?
How to find and define the objective for control system ?
such as how to find Q and R for objective?
which book teaching this?
0
votes
1answer
58 views
2nd Order Optimal Control Problem
I'm working on a homework problem in optimal controls and my plant model is described as:
$$\ddot{x}(t) = u(t)$$
The performance index (cost function) is described by:
$$J = 1/2\int_0^5u^{2}(t)dt\,$$
...
0
votes
0answers
43 views
Which book teaching simplex algorithm for matrix?
For H2 or H infinity, find K which minimize
| Ws*So |
| Wks*K*So|
would like to know simplex algorithm for matrix or any other method which solve above ...
4
votes
1answer
304 views
Difference between Bellman and Pontryagin dynamic optimization?
Can someone please explain the difference between dynamic optimization via the Bellman equation and dynamic optimization via Pontryagin's maximization principle?
Thanks
