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An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time. A typical algebraic Riccati equation is similar to one of the following: the continuous time algebraic Riccati equation (CARE):
The finite horizon version of this is a convex optimization problem, and so the problem is often solved repeatedly with a receding horizon. This is a form of model predictive control . [ 5 ] [ 6 ]
A particular form of the LQ problem that arises in many control system problems is that of the linear quadratic regulator (LQR) where all of the matrices (i.e., , , , and ) are constant, the initial time is arbitrarily set to zero, and the terminal time is taken in the limit (this last assumption is what is known as infinite horizon). The LQR ...
The method of undetermined coefficients, also known as 'guess and verify', can be used to solve some infinite-horizon, autonomous Bellman equations. [14] The Bellman equation can be solved by backwards induction, either analytically in a few special cases, or numerically on a computer.
The objective is to choose a policy that will maximize some cumulative function of the random rewards, typically the expected discounted sum over a potentially infinite horizon: E [ ∑ t = 0 ∞ γ t R a t ( s t , s t + 1 ) ] {\displaystyle E\left[\sum _{t=0}^{\infty }{\gamma ^{t}R_{a_{t}}(s_{t},s_{t+1})}\right]} (where we choose a t = π ( s ...
The one other assumption of the model is that the firm uses an infinite horizon when it calculates the present value of future cash flows. Although no firm actually has an infinite horizon, the consequences of assuming one are discussed in the following. [2] Under the assumptions of the model, CLV is a multiple of the margin.
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A Rubinstein bargaining model refers to a class of bargaining games that feature alternating offers through an infinite time horizon. The original proof is due to Ariel Rubinstein in a 1982 paper. [1]