Simulation of optimal control on pollution of environment (Q2703283)

The article deals with a macromodel of an ecological-economical system with piecewise linear macroproduction function NEWLINE\[NEWLINE\int_{t_0}^{t_{m}}q(c,z)e^{-\sigma t} dt\to \max_{u,v},NEWLINE\]NEWLINE NEWLINE\[NEWLINE\dot k=(1-u-v)f(k)-\mu k, \qquad \dot z=(d-\lambda v) f(k)-\nu z,NEWLINE\]NEWLINE \(k(t_0)=k^{(0)},\;k(t_{m})\geq k^{(m)},\;z(t_0)=z^{(0)} \in Z_0(t_0),\;z(t_{m})\leq z^{(m)}\in Z_{m}(t_{m}),\;u_0\leq u \leq u_1\),NEWLINENEWLINENEWLINE\(v_0\leq v\leq v_1,\) where \(k\) are the available funds; \(c\) and \(z\) are the corresponding specific indexes of consumption and pollution; \(u\) is the consumption part of the specific final product \(y=f(k)\); \(v\) is the part of the final product which is used for pollution control; \(0<\mu<1\) is the coefficient of capital amortization; \(0<d<1\) is the part of production pollution of the total value of the final product; \(\lambda>1\) is the quantity of pollution units destroyed by one unit of the final product; \(0<\nu<1\) is the coefficient of natural reduction of pollution; \(Z_0(t_0)\), \(Z_{m}(t_{m})\) are the sets of admissible initial and terminal values of pollution; \(f(k)\) is a macroproduction piecewise linear function; \(q(c,z)\) is the efficiency function of the ecological-economical process. Algorithms of construction of the optimal control program are considered.