  An innovative numerical algorithm for solving infinite-horizon optimal
control problems is introduced in this paper, using the IsoCost-HyperSurface
(ICHS) concept. In the state space of an optimal control system, an ICHS is
defined as a set of state points having a certain amount of the cost value. In
this paper, it is proved that for a certain cost amount, the ICHS resulting
from the infinite-horizon optimal control solution, surrounds all other ICHSs
resulting from non-optimal control strategies. Regarding this geometric
feature, the novel Isocost Dynamic Programming (IDP) algorithm is introduced to
search for optimal control solutions. As an illustration of the introduced ICHS
concepts and to demonstrate the effectiveness of the proposed IDP algorithm,
several simulated examples are presented. The results are compared with those
of conventional DP. These comparisons demonstrate that the proposed algorithm
has better relative optimality compared to the DP algorithm with 18% lower
cumulative cost value, by comparing results from the closed-loop control of two
nonlinear systems with random initial conditions. More significantly, when
compared to the DP algorithm, the IDP was able to enhance computational
performance by reducing the execution time by 21 % while using less memory.
