Based on the polynomial representation of the system, we formulate a feasibility problem that can be solved efficiently by semi-definite programming.
By viewing phenotype formation as an evolutionary system, we formulate mathematical equations to model the ecological mechanisms that drive the interaction and coordination of its constituent components toward population dynamics and stability.
Taking into account the time variant and dynamic features of this system, we formulate the problem as a stochastic network optimization problem and solved by Lyapunov optimization approach initially developed in [30, 31].
To describe the behavior of the system, we formulate differential equations in the standard way by ignoring variants in cell density (caused by cell growth and division, for example).
Based on a recently developed notion of physical realizability for quantum linear stochastic systems, we formulate a quantum LQG optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum.
Besides, according to the second and the fourth equations of the system (2), we formulate the following two comparison systems: left { textstylebegin{array}{l@{quad}l} frac{dI_{1}(t)}{dt} = -d_{i} I_{1}(t),& tneq ktau, I_{1}(t^)=I_{1}(t)+sigma,& t=ktau, I_{1}(0^)=I_{0}>0 end{array}displaystyle right.
To study the system numerically, we formulate a semi-implicit scheme that is able to preserve the particle maximum packing fraction.
To determine the cost incurred for the system operation, we formulate a cost function involving some cost elements associated with different states of the machining system.
Based on the unified hybrid system model, we formulate the aggregated control problem as an optimal control problem, which seeks for an optimal energy usage plan for a population of heterogeneous loads.
Therefore, to improve the system efficiency, we formulate the emission control problem as a cooperative game using the Nash bargaining solution in next subsection.
